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LECTURE NOTES in HS PHYS 001

GENERAL PHYSICS 1 Name

: _______________________________________________________

Section

: _______________________________________________________

Professor

: _______________________________________________________

HS PHYS 001 GENERAL PHYSICS 1 Topic:

1. 2. 3. 4.

MEASUREMENTS

Intended Learning Outcomes: Distinguish between Fundamental and Derived Quantities Write numbers in Scientific Notations Determine Significant Figures of a given quantity Convert one unit to another

Fundamental Quantities -

Physical quantities that cannot be defined in terms of other physical quantities.

Examples: 1000 m 5,000,000 g 0.000007 s

= 1 x 103 m = 5 x 106 g = 7 x 10-6 s

= 1 kilometer = 5 megagram = 7 microsecond

= 1 km = 5Mg = 7µs

In Mechanics, the three Fundamental Quantities are: 1. Length 2. Mass 3. Time The SI (Système International) Units  Meter, m ( for LENGTH) - distance travelled by light in vacuum during a time interval 1/299 792 458 second.  Kilogram, kg (for MASS) - the mass of a specific Platinum-Iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sevres, France.  Second, s (for TIME) - 9 162 631 770 times the period of vibration of radiation from the Cesium – 133 atom. Other SI fundamental Units 4. Temperature (Kelvin) 5. Electric Current (Ampere) 6. Luminous Intensity (Candela) 7. Amount of Substance (mole)

Derived Quantities - Quantities that are based on the result of a systematic equation that includes any of the seven basic quantities Examples: Volume V = length x width x height Density ρ = mass / volume Area A = length x width Prefixes for Powers of Ten 103 kilo (K) 106 mega (M) 109 giga (G) 1012 tera (T) 1015 peta (P) 1018 exa (E) 1021 zetta (Z) 1024 yotta (Y)

10-24 10-21 10-18 10-15 10-12 10-9 10-6 10-3 10-2 10-1

Significant Figures m3

unit: unit: kg/m3 unit: m2

yocto (y) zepto (z) atto (a) femto (f) pico (p) nano (n) micro (µ) milli (m) centi (c) deci (d)

-

express a magnitude to a specified degree of accuracy, rounding up or down the final figure

Rules: 1) All nonzero digits are significant. Ex. 253.167 (6 SF) 2) All zeroes between significant digits are significant. Ex. 103.05 (5 SF) 3) Leading zeros are not significant. Ex. 0.008 (1 SF) 4) Trailing zeros to the right of the decimal point are significant. Ex. 27.00 (4 SF) 5) Trailing zeros in a whole number with the decimal point shown are significant. Ex. 370. (3 SF) 6) Trailing zeros in a whole number with no decimal point shown are not always significant. Ex. 3700 (2, 3, or 4 SF) 7) For a scientific notation, the powers of ten is not significant. Ex. 9.3 x 105 (2 SF)

Examples: Determine the number of significant figure 1. 3.1451 9. 0.0008 2. 2.0506 10. 0.0010 3. 254.0 11. 1.2 x 10-5 4. 254.00 12. 3.70 x 107 5. 250.0 13. 3.700 x 107 6. 260. 14. 0.006040 7. 260 15. 4 x 103 8. 2600 16. 10201 Answers: 1. _____ 2. _____ 3. _____ 4. _____ 5. _____ 6. _____ 7. _____ 8. _____

9. 10. 11. 12. 13. 14. 15. 16.

_____ _____ _____ _____ _____ _____ _____ _____

Conversion of Units

Unknown Quantity

=

Known x Conversion Quantity Factor

Addition and Subtraction: 1. Perform all the operations 2. Round off result so that you include only 1 uncertain digit. Example: 153. ml + 1.8 ml + 9.16 ml = 163.96 ml Answer = 164 ml (3 SF, uncertain digit = ones place) Multiplication and Division: 1. Perform all the operations 2. Round off the result so that it has the same number of significant figure as the least of all those used in calculation. Example: (2.5 m) x (2.01 m) x (2.755 m) = 13.843875 m3 Answer: 14 m3 (2 sig figs)

Examples: Covert the following: 1. 15.0 in → cm 2. 38.0 m/s → mi/hr 3. 4.850 kg → lb 4. 3.0 L → cm3 5. 1.25 gal →ft3 6. A pyramid has a height of 481 ft and its base covers an area of 13.0 acres. The volume of a pyramid is given by the expression V=1/3 Bh, where B is the area of the base and h is the height. Find the volume of the pyramid in cubic meters. (1 acre = 43 560 ft2) Solution:

HS PHYS 001 GENERAL PHYSICS 1 Topic:

MEASUREMENTS

Written Work No. ____ Name : _______________________________________ Section: __________________________________ Date: __________________________

I.

Write the number of Significant Figures 1. 2.345 - _____________ 2. 1.20 - _____________ 3. 0.005 - _____________ 4. 0.40560 - _____________ 5. 0.00000170 - _____________ 6. 23600 - _____________ 7. 1.750 x 106 - _____________ 8. 2.0 x 10-7 - _____________ 9. 16.00 x 1013 - _____________ 10. 8075.2 - _____________

2.

An ore loader moves 1200 tons/hr from a mine to the surface. Convert this rate to pounds per second, using 1 ton = 2000 lb.

3.

A rectangular building lot has a width of 75.0 ft and a length of 125 ft. Determine the area of this lot in square meters.

4.

36.85 kg of starch was added to 12.3 kg of sugar, 86.123 kg of water and 4.0001 kg of egg. Determine the total mass of the ingredients.

II. Use numbers 1-5 to rank the following, 1 as the largest and 5 as the smallest. If two of the masses are equal, give them equal rank. _____ 0.032 kg _____ 15 g _____ 2.7 x 105 mg _____ 4.1 x 10-8Gg _____ 2.7 x 108𝜇g

III. Solve the following Problems: (Box all final answers, follow significant figures, indicate the corresponding units) 1.

A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm3. From these data, calculate the density of lead in SI units (kilogram per cubic meter).

HS PHYS 001GENERAL PHYSICS 1 Topic:

VECTORS

Intended Learning Outcomes: 1. Differentiate vector and scalar quantities 2. Perform addition of vectors 3. Rewrite a vector in component form 4. Calculate directions and magnitudes of vectors

REVIEW ON TRIGONOMETRY

Pythagorean theorem: Note: For Right Triangle Only

h 2  ho2  ha2 Oblique Triangle– Triangle with NO 90°-angle

Trigonometric Function:

sin  

ho h soh  cah  toa

cos  

ha h cho  sha  cotao

Example 1

tan  

ho ha

Example 1

Example 3

A building casts a shadow 67.2m away from the building. The angle of inclination from the ground to the top of the building is 50°. Determine the height of the building.

A bicycle race follows a triangular course. The 3 legs of the race are in order, 2.3 km, 5.9 km, and 6.2 km. Find the angle between the starting leg and the finishing leg, to the nearest degree.

Example 4 Example 2 A runaway dog walks 0.64 km due north. He then runs due west to a hot dog stand. If the magnitude of the dog's total displacement vector is 0.91 km, what is the magnitude of the dog's displacement vector in the due west direction.

The sides of a triangular lot are 130 m, 180 m, and 190 m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line.

SCALARS AND VECTORS Scalar Quantities

described by a single number, pertains to magnitude only Examples: II. temperature, 98° C III. speed, 35 m/s IV. mass, 80 kgs. Vector Quantities a physical quantity that inherently with both magnitude and direction Examples: 11. velocity, 35 m/s North of East 12. force, 35 N rightward 13. displacement, 40 m from the origin 14. gravitational pull of man to earth Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector while the length of a vector arrow is proportional to the magnitude of the vector.

EXAMPLE 1

4 lb 8 lb

EXAMPLE 2

Resultant Vector Often it is necessary to add one vector to another. The combined effect of adding to or more vector is called resultant or resultant vector denoted by “R”.

Vector Representation: An arrow is used to represent a vector. The arrowhead gives the direction and the entire length of the arrow represents the vector’s magnitude. A scale is necessary to express the vector’s magnitude in length units. EXAMPLES: 1. 5km, east Scale: 1km = 1cm

2. 300N, 120° Scale: 50N = 1cm

EXAMPLE 2. Solve using triangle method A = 50 N, 25o N of E B = 70 N, 80o N Req’d: Find R = A + B

3. 120KPH, 60° north of east Scale: 60KPH = 1inch

Methods in Finding the Resultant Vector: 5.

by Triangle Method -Two forces are represented by their free vectors placed tip to tail, their resultant vectoris the third side of the triangle. -The direction of the resultantbeing from the tail of the first vector to the tip of the last vector.

EXAMPLE 1. Solve using graphical approach A = 50 N, 25o N of E B = 70 N, 80o N Req’d: Find R = A + B Use Scale: 1 cm : 10 N

II.

by Parallelogram Method

1.

The resultant of two forces is the diagonal of the parallelogram formed on the vectors of these forces.

2.

Vectors are combined tail-to-tail.

3.

It involves properties of parallelogram and can be solved using laws of sine and cosine.

EXAMPLE 3. Solve using parallelogram method A = 50 N, 25o N of E B = 70 N, 80o N Req’d: Find R = A + B

III.

by Polygon Method a.

The head-to-tail method to calculate a resultant that involves lining up the head of one vector to the tail of the other

b.

The resultant vector is determined using a ruler and protractor.

EXAMPLE 4. Solve using polygon method A = 50 km, 0o with respect to X-Axis B = 80 km, 40o Above X-Axis C = 40 km, 140o Above X-Axis D = 30 km, 160o Below X-Axis Req’d: Find R = A + B + C + D Scale: 1 cm : 10 km

The vector components of ⃗𝑨 ⃗⃗ are two 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 ⏊ vectors ⃗⃗⃗⃗⃗ 𝐴𝑥 and ⃗⃗⃗⃗⃗ 𝐴𝑦 that are parallel //to ⃗⃗⃗ = ⃗⃗⃗⃗⃗ the x and y axes, and add together so that 𝑨 𝑨𝒙 + ⃗⃗⃗⃗⃗ 𝑨𝒚 . 





Ax  A cos  

  tan 1 (



Ay  A sin  

A

IV.

by Component Method c.

the most accurate way of finding the resultant vector. Each given vector is resolved into its x and y components.

 2



Ax  2

Ax  Ay

EXAMPLE 5. Solve using component method A = 50 N, 25o N of E B = 70 N, 80o N Req’d: Find R = A + B

EXAMPLE 6. Solve using polygon method A = 50 km, 0o with respect to X-Axis B = 80 km, 40o Above X-Axis C = 40 km, 140o Above X-Axis D = 30 km, 160o Below X-Axis 𝑥⃗ and 𝑦⃗ are called the 𝒙 vector component/horizontal component and ⃗⃗ the 𝒚 vector component/vectical component of 𝒓

Ay

Req’d: Find R = A + B + C + D

)

HS PHYS 001 GENERAL PHYSICS 1 Topic:

VECTORS

Written Work No. ____ Name : _______________________________________ Section: __________________________________ Date: __________________________

SOLVE EACH PROBLEM. 1.

A car travels 20.0 km due north and then 35.0 km in a direction 60.0° west of north. Find the magnitude and direction of the car’s resultant displacement.

2.

A sailboat leaves a harbor and sails 1.8 km in the direction 65° south of east, where the captain stops for lunch. A short time later, the boat sails 1.1 km in the direction 15° north of east. What is the magnitude of the resultant displacement from the harbor?

3.

A displacement vector has a magnitude of 175m and points at an angle of 50.0 degrees relative to the x axis. Find the x and y components of this vector.

4.

Find the magnitude and direction of resultant of the figure shown below. Also, find its horizontal and vertical component.

5.

Use the component method of vector addition to find the components of the resultant of the four displacements shown in the figure. The magnitudes of the displacements are: A = 2.25 cm, B = 6.35 cm, C = 5.47 cm, and D = 4.19 cm.

HS PHYS 001 GENERAL PHYSICS 1 Topic:

UNIT VECTOR

Intended Learning Outcomes: 1. 2. 3.

Define a unit vector. Distinguish a unit vector from ordinary vector. Solve unit vector problems.

UNIT VECTOR d. A vector that has a magnitude of 1, with no units. e. It is used to describe a direction in space. f. It is expressed with a caret or “hat” (^) to distinguish it from ordinary vectors. g. Notation: |𝑢̂|= 1 𝑖̂- unit vector that has a magnitude of 1 and points in the direction of x-axis; (1,0,0)

⃗⃗ = 𝑨 ⃗⃗⃗ + 𝑩 ⃗⃗⃗ 𝑪 where, ⃗𝑨 ⃗⃗ = 𝑨𝒙 𝒊 + 𝑨𝒚 𝒋 ⃗⃗⃗ = 𝑩𝒙 𝒊 + 𝑩𝒚 𝒋 𝑩 then, ⃗⃗ =(𝑨𝒙 𝒊 + 𝑩𝒙 𝒊) + ( 𝑨𝒚 𝒋+𝑩𝒚 𝒋) 𝑪 ⃗𝑪⃗ = √𝑪𝒙 𝟐 + 𝑪𝒚 𝟐

𝑗̂- unit vector that has a magnitude of 1 and points in the direction of y-axis; (0,1,0) 𝑘̂ - unit vector that has a magnitude of 1 and points in the direction of z-axis; (0,0,1)

EXAMPLES - Given the two displacements 𝐷 = (6𝑖 + 3𝑗 − 𝑘)𝑚 𝑎𝑛𝑑 𝐸 = (4𝑖 − 5𝑗 + 8𝑘)𝑚, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 2𝐷 − 𝐸.

-

Arrange the following vectors in order of their magnitude, with the vector of the largest magnitude first. (a) 𝐴 = 3𝑖 + 5𝑗 − 2𝑘)𝑚; (𝑏) 𝐵 = (−3𝑖 + 5𝑗 − 2𝑘)𝑚; (𝑐) 𝐶 = (3𝑖 − 5𝑗 − 2𝑘)𝑚; (𝑑) 𝐷 = (3𝑖 + 5𝑗 + 2𝑘)𝑚.

⃗⃗ lying in the Find the sum of two displacement vectors 𝐴⃗ and 𝐵 ⃗ ⃗⃗ (2.0𝑖̂ ) (2.0𝑖̂ xy plane given by 𝐴 = + 2.0𝑗̂ 𝑚 and 𝐵 = − 4.0𝑗̂)𝑚.

-

Also, 



A  B  Ax B x  Ay B y  Az B z Scalar/Dot Product in terms of Components Note: ⃗⃗ ● ⃗𝑩 ⃗⃗ = 𝟎. If angle 𝜃 is 90° or perpendicular, ⃗𝑨 If 90 < 𝜃 ≤ 180°, scalar is negative. If 0 ≤ 𝜃 < 90°, scalar is positive.

A particle undergoes three consecutive displacements:. ∆𝑟⃗⃗⃗⃗1 = (15𝑖̂ + 30𝑗̂ + 12𝑘̂)𝑐𝑚, ∆𝑟⃗⃗⃗⃗2 = (23𝑖̂ − 14𝑗̂ − 5.0𝑘̂)𝑐𝑚 and ∆𝑟⃗⃗⃗⃗3 = (−13𝑖̂ + 15𝑗̂)𝑐𝑚.Find the unit-vector notation for the resultant displacement and its magnitude.

-

Example 1 ⃗⃗ are given by 𝐴⃗ = 5𝑖̂ + 2𝑗̂ − 3𝑘̂ and 𝐵 ⃗⃗ = 4𝑖̂ − 3𝑗̂ + The vectors 𝐴⃗ and 𝐵 ̂ 10𝑘. ⃗⃗. a.) Determine the magnitude of 𝐴⃗ and 𝐵 ⃗ ⃗⃗. b.) Determine the scalar product 𝐴 ● 𝐵 ⃗⃗. c.) Find the angle between 𝐴⃗ and 𝐵

Scalar Product / Dot Product Scalar Product also called Dot Product -

⃗⃗denoted by 𝐴⃗ ● 𝐵 ⃗⃗ scalar product of vectors 𝐴⃗and 𝐵 it is a scalar quantity equal to the product of the magnitudes of the two vectors and the cosine of the angle 𝜃 between them

Example 2 ⃗⃗ and B ⃗⃗ = 2î + 3ĵ and B ⃗⃗ are given by A ⃗⃗ = −î + 2ĵ. a.) The vectors A ⃗ ⃗ ⃗⃗⃗⃗ Determine the scalar product A ● B. b.) Find the angle between ⃗A⃗ and ⃗⃗. B

-

⃗⃗onto 𝐴⃗ 𝐴⃗multiplied by 𝐵𝑐𝑜𝑠𝜃, which is the projection of 𝐵 The scalar product is commutative, that is ⃗⃗⃗ ● 𝑩 ⃗⃗⃗ = 𝑩 ⃗⃗⃗●𝑨 ⃗⃗⃗ 𝑨 and also obeys the distributive law of multiplication, ⃗⃗) = 𝑨 ⃗⃗ ⃗⃗⃗ ● (𝑩 ⃗⃗⃗ + 𝑪 ⃗⃗⃗ ● 𝑩 ⃗⃗⃗ + 𝑨 ⃗⃗⃗ ● 𝑪 𝑨

Vector Product / Cross Product Vector Product also called Cross Product -

⃗⃗⃗and 𝑩 ⃗⃗⃗denoted by 𝑨 ⃗⃗⃗ 𝒙 𝑩 ⃗⃗⃗ vector product of vectors 𝑨 it is a vector quantity equal to the product of the magnitudes of the two vectors and the sine of the angle 𝝓 between them ⃗⃗ = 𝑨 ⃗⃗⃗ 𝒙 𝑩 ⃗⃗⃗ 𝑪

Note: ⃗⃗ and ⃗𝑩 ⃗⃗are parallel or coincident (same angle), φ= 𝟎, and ⃗𝑨 ⃗⃗ 𝒙 ⃗𝑩 ⃗⃗ = 𝟎. If vector ⃗𝑨 ⃗⃗ = 𝟎. If φ= 𝟎°or φ= 𝟏𝟖𝟎°, vector product, 𝑪 ̂ 𝒊̂ 𝒙 𝒌 ̂ = −𝒋̂ 𝒊̂ 𝒙 𝒊̂ = 𝟎 𝒊̂ 𝒙 𝒋̂ = 𝒌 ̂ = 𝒊̂𝒋̂ 𝒙 𝒊̂ = −𝒌 ̂ 𝒋̂ 𝒙 𝒋̂ = 𝟎 𝒋̂ 𝒙 𝒌 ̂ ̂ ̂ ̂ 𝒌 𝒙 𝒌 = 𝟎𝒌 𝒙 𝒊̂ = 𝒋̂𝒌 𝒙 𝒋̂ = −𝒊̂ ⃗⃗⃗ 𝒙 𝑩 ⃗⃗⃗ ≠ 𝑩 ⃗⃗⃗ 𝒙 ⃗𝑨 ⃗⃗ (commutative property does not apply). 𝑨 ⃗ ⃗⃗ ⃗ ⃗⃗ ⃗⃗⃗ 𝒙 ⃗𝑨 ⃗⃗. and that, 𝑨 𝒙 𝑩 = −𝑩      A x B  ( Ay B z  Az B y ) i  ( Ax B z  Az B x ) j  ( Ax B y  Ay B x ) k

The vector product can also be expressed in determinant form,

𝒊̂ ⃗𝑨 ⃗⃗ 𝒙 ⃗𝑩 ⃗⃗ = | 𝑨𝒙 𝑩𝒙

𝒋̂ 𝑨𝒚 𝑩𝒚

̂ 𝒌 𝑨𝒛 | 𝑩𝒛

Example 3 ⃗⃗ = 4𝑖̂ − 3𝑗̂ + 10𝑘̂. a.) Find the magnitude of the vector product of 𝐴⃗ = 5𝑖̂ + 2𝑗̂ − 3𝑘̂ and 𝐵 ⃗⃗. b.) Find the angle between vectors 𝐴⃗ and 𝐵

HS PHYS 001 GENERAL PHYSICS 1 Topic:

UNIT VECTORS

Written Work No. ____ Name : _______________________________________ Section: __________________________________ Date: __________________________

SOLVE EACH PROBLEM. -

-

Given two vectors 𝐴 = 4𝑖 + 3𝑗 𝑎𝑛𝑑 𝐵 = 5𝑖 − 2𝑗 (a) find the magnitude of each vector, (b) write an expression for the vector difference 𝐴 − 𝐵 using unit vectors; and (c) find the magnitude and direction of the vector difference 𝐴 − 𝐵.

-

⃗⃗ are given by 𝐴⃗ = 6𝑖̂ + 2𝑗̂ − 𝑘̂ and 𝐵 ⃗⃗ = The vectors 𝐴⃗ and 𝐵 ̂ 5𝑖̂ − 𝑗̂ + 8𝑘.

-

⃗⃗. a.) Determine the magnitude of 𝐴⃗ and 𝐵 ⃗ ⃗⃗ b.) Determine the scalar product 𝐴 ● 𝐵. ⃗⃗. c.) Find the angle between 𝐴⃗ and 𝐵

Find the magnitude of the vector product of 𝐴⃗ = 2𝑖̂ + 2𝑗̂ − 𝑘̂ ⃗⃗ = 3𝑖̂ − 6𝑗̂ + 2𝑘̂ and find the angle between vectors 𝐴⃗ and 𝐵 ⃗⃗. and 𝐵

Given the two displacements 𝐷 = (4𝑖 + 3𝑗 − 𝑘)𝑚 𝑎𝑛𝑑 𝐸 = (2𝑖 − 5𝑗 + 2𝑘)𝑚, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 2𝐷 − 𝐸.

HS PHYS 001 GENERAL PHYSICS 1 Topic:

Kinematics in One Dimension

Intended Learning Outcomes: 1. Convert a verbal description of a physical situation involving uniform acceleration in one dimension into a mathematical description 2. Recognize whether or not a physical situation involves constant velocity or constant acceleration 3. Construct v vs. t and a vs. t graphs, respectively, corresponding to a given position vs. time-graph and velocity vs. time graph and vice versa. 4. Use the fact that the magnitude of acceleration due to gravity on the Earth’s surface is nearly constant 9.8 m/s2 in free-fall problems 5. Solve for unknown quantities in equations involving one-dimensional uniformly accelerated motion 6. Solve problems involving one-dimensional motion with constant acceleration in contexts such as, but not limited to, the “tail-gating phenomenon”, pursuit, rocket launch, and free- fall problems

Introduction Engineering Mechanics – science which considers the effects of forces on rigid bodies Dynamics – deals with the effect that forces have on motion Kinematics – (same root as cinema) geometry of motion, without consideration of force causing motion Kinetics – relates the force acting on a body to its mass and acceleration Statics – considering the effects and distribution of forces on rigid bodies (bodies at rest and remain at rest or in a fixed position)

Note: For horizontal motion, right direction Is (+) and left direction is (-)

Engineerin g Mechanics  Statics Dynamics      Force Systems Applicatio ns Kinematics Kinetics            Concurrent Trusses Translatio n Translatio n Parallel Non  Concurrent

Centroids Friction

Rotation Rotation Plane Motion Plane Motion

Displacement and Distance As an object moves, its position changes with time.

Displacement ∆x- change in position specified by length and direction, a vector quantity. Distance, d- a length from one point another usually measured in a straight line, a scalar quantity.

Speed and Velocity

TABLE 1. Position of the Car at various times. Example 1 Find the displacement, average velocity, and average speed of the car between positions A and F as described by the Table 1.

GRAPH 1. Position Vs. Time Graph

Example 2 Distance Run by a Jogger How far does a jogger run in 1.5 hours if his average speed is 2.22 m/s?

Example 3 World’s Fastest Jet-Engine Car Andy Green in the car ThrustSSC set a world record of 341.1 m/s in 1997. To establish such a record, the driver makes two runs through the course, one in each direction, to nullify wind effects. From the data, determine the average velocity for each run.

GRAPH 2. Position Vs. Time Graph

Example 2 A position–time graph for a particle moving along the xaxis is shown in the figure below. (a) Find the average velocity in the time interval t = 1.50 s to t = 4.00 s. (b) Determine the instantaneous velocity at t = 2.00 s by measuring the slope of the tangent line shown in the graph. (c) At what value of t is the velocity zero?

Acceleration Acceleration – change in velocity per unit time

Example 1 Determine the average acceleration of the plane.

 vo  0 m s to  0 s

 v  260 km h t  29 s

Example 2

Example 3

Constant Acceleration

Equations of Kinematics for Constant Acceleration

Example 1 An airplane travels 800 m down the runway before taking off. It starts from rest, moves with constant acceleration, and becomes airborne in 20 s, what is its speed when it takes off?

Example 4 A car moving at 20 m/s slows down at 1.5 m/s2 to a velocity of 10 m/s. How far did the car go during the slowdown? How long did it last?

Freely Falling Bodies

Example 2 Catapulting a Jet Find its displacement.

(a) Air Filled Tube (b) Evacuated Tube

Example 3 A bus travels 400 m between two stops. It starts from rest and accelerates at 1.5 m/s2 until it reaches a velocity of 9.0 m/s. The bus continues at this velocity and then decelerates at 2.0 m/s2 until it comes to a halt. Find the total time required for the journey.

Example 1 A stone thrown from the top of a building is given an initial velocity of 20.0 m/s straight upward. The building is 50.0 m high, and the stone just misses the edge of the roof on its way down, as shown in the figure.

Example 2 If a frog can jump straight up to a height of 0.52 m, what is its initial speed as it leaves the ground? For how much time is it in the air?

Example 3 A book accidentally falls from a shelf 4.2 m high. A librarian is standing nearby and moves 0.80 m, starting from rest, to catch the book. What must be his average acceleration if he catches the book when it is 1.8 m above the floor?

b.) Find the maximum height of the stone. c.) Determine the velocity of the stone when it returns to the height from which it was thrown. d.) Find the velocity and position of the stone at t = 5.00 s.

Example 4 A ball is dropped from a balloon that is rising vertically at 30 m/s. If the ball reaches the ground in 10 secs. a.) Find the highest point reached by the ball and the time of flight. b.) Determine the height of the balloon above the ground when the ball dropped and the velocity of the ball as it strikes the ground.

HS PHYS 001 GENERAL PHYSICS 1 Topic:

One Dimensional Kinematics Written Work No. ____

Name : _______________________________________ Section: __________________________________ Date: __________________________

1.

A car moves 65 km due East then 45 km due West. What is its total displacement? 9. If a car accelerates from rest at a constant 5.5 m/s2, how long will it need to reach a velocity of 28 m/s?

2. You drive a car for 2.0 h at 40 km/h, then for another 2.0 h at 60 km/h. What is your average velocity? 10. A car slows from 22 m/s to 3.0 m/s at a constant rate of 2.1 m/s2. How many seconds are required before the car is traveling at 3.0 m/s? 3. An Indy 500 race car’s velocity increases from +4.0 m/s to +36 m/s over a 4.0s time interval. What is its average acceleration? 11. A spaceship far from any star or planet accelerates uniformly from 65.0 m/s to 162.0 m/s in 10.0 s. How far does it move? 4. The race car slows from +36 m/s to +15 m/s over 3.0 s. What is its average acceleration? 12. A particle’s motion is described by the equation (𝑡)=3𝑡2+5𝑡+2 . What is the particle’s velocity at t = 4s? 5. A car is coasting downhill at a speed of 3.0 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at a speed of 4.5 m/s. Assuming that uphill is the positive direction, what is the car’s average acceleration?

13. A car is stopped at the traffic light. It then travels along a straight road so that its distance from the light is given by 𝑥(𝑡)=(2.40𝑚/𝑠2 )𝑡2−(0.120𝑚/𝑠3) 𝑡3. a. Calculate the average velocity of the car for the time interval t = 0s to t = 10.0s

6. A bus is moving at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0 s. What is the average acceleration of the bus while braking?

7. A golf ball rolls up a hill toward a miniature-golf hole. Assign the direction toward the hole as being positive. If the ball starts with a speed of 2.0 m/s and slows at a constant rate of 0.50 m/s2, what is its velocity after 2.0 s?

b. Calculate the instantaneous velocity of the car at t = 0s, t = 5.0s and t = 10.s.

14. The acceleration of a particle is given by 𝑎(𝑡)=(−2.00𝑚/𝑠2)+(3.00𝑚/𝑠3) 𝑡3. Find the initial velocity of the particle such that it will have the same x-coordinate at t = 4.00s as it had at t = 0s

8. A bus, traveling at 30.0 km/h, speeds up at a constant rate of 3.5 m/s2. What velocity does it reach 6.8 s later? REFERENCE: General Physics 1 by. Marasigan D.E.

HS PHYS 001 GENERAL PHYSICS 1 Topic:

1. 2. 3. 4. 5. 6. 7. 8.

Kinematics in Two Dimension

Intended Learning Outcomes: Describe motion using the concept of relative velocities in 1D and 2D Extend the definition of position, velocity, and acceleration to 2D and 3D using vector representation Deduce the consequences of the independence of vertical and horizontal components of projectile motion Calculate range, time of flight, and maximum heights of projectiles Differentiate uniform and non-uniform circular motion Infer quantities associated with circular motion such as tangential velocity, centripetal acceleration, tangential acceleration, radius of curvature Solve problems involving two dimensional motion in contexts such as, but not limited to ledge jumping, movie stunts, basketball, safe locations during firework displays, and Ferris wheels Plan and execute an experiment involving projectile motion: Identifying error sources, minimizing their influence, and estimating the influence of the identified error sources on final results

Projectile Motion Projectile – an object given an initial velocity and follows a parabolic path (called trajectory) determined entirely by the effects of gravitational acceleration neglecting air resistance.

The vertical components are affected by gravitational acceleration. The horizontal components are not affected by any acceleration.

Note: 𝒚 is (+) above reference line 𝒚 is (−) below reference line 𝑽𝒇𝒚 is (+) going upward 𝑽𝒇𝒚 is (−) going downward 𝑽𝒇𝒚 is 𝟎 at maximum height, 𝒚𝒎𝒂𝒙

Where: 𝑽𝒊 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑽𝒊𝒙 = ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑽𝒊𝑦 = 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝜽 = 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒 𝑤𝑖𝑡ℎ 𝑟𝑒𝑠𝑝𝑒𝑐𝑡 𝑡𝑜 𝑥 − 𝑎𝑥𝑖𝑠

CASES OF PROJECTILE CASE 1. HORIZONTALLY LAUNCH

CASE 2. LAUNCH AT AN ANGLE AT THE GROUND

CASE 3. LAUNCH AT AN ANGLE ABOVE A CERTAIN HEIGHT.

Example 1 A long jumper leaves the ground at an angle of 20.0° above the horizontal at a speed of 11.0 𝑚/𝑠. a.) How far does he jump in the horizontal direction? b.) What is the maximum height reached? Example 2 A baseball is thrown at an angle of 60° above the horizontal, strikes a building 36.0 𝑚 away at a point 8𝑚 above the point from which it is thrown. a.) Find the magnitude of the initial velocity of the baseball (from which it was thrown) b.) Find the magnitude and direction of the velocity of the baseball before it strikes the building. Example 3 A projectile is fired from the top of a cliff 300 𝑓𝑡. High with a velocity of 1414 𝑓𝑡/𝑠 directed at an angle of 45° to the horizontal. Find the range on a horizontal plane through the base of the cliff. Example 4 A ball is thrown horizontally from the roof of a building 20𝑚 high at 25 𝑚/𝑠. a.) How far from the building will it strike the ground? b.) What will be the ball’s velocity when it strikes the ground?

NOTE: 𝟐𝒔𝒊𝒏𝜽𝒄𝒐𝒔𝜽 = 𝒔𝒊𝒏𝟐𝜽

Example 5 A cannonball is fired at an angle of 30.0° with the horizontal. It lands 60𝑚. measured horizontally and 2𝑚 below measured vertically from its point of release. Determine the initial velocity of the stone (𝑖𝑛 𝑚/𝑠).

Uniform Circular Motion Uniform Circular Motion– objects that move in a circular path with constant speed but direction of velocity is not constant.

𝒗 = 𝑠𝑝𝑒𝑒𝑑/𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑚/𝑠 𝟐𝝅𝒓 = 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟, 𝑚 𝑻 = 𝑡𝑖𝑚𝑒 𝑜𝑟 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 𝑡𝑜 𝑚𝑎𝑘𝑒 𝑜𝑛𝑒 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛, 𝑎𝑙𝑠𝑜 𝑐𝑎𝑙𝑙𝑒𝑑 𝒑𝒆𝒓𝒊𝒐𝒅, 𝑠

𝒇 = 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚, 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒𝑑 𝑏𝑦 𝑎𝑛 𝑜𝑏𝑗𝑒𝑐𝑡, 𝐻𝑧

Example 1 The wheel of a car has a radius of 0.29m and it is being rotated at 830 revolutions per minute on a tire-balancing machine. Determine the speed at which the outer edge of the wheel is moving.

Example 2 An electric fan rotates at 800 rev per min. Consider a point on the blade a distance of 0.16m from the axis. Calculate the speed at this point and its centripetal acceleration.

Centripetal Force – the force (real force) on the body towards the center of rotation when the body is moving around a curved path. Centrifugal Force – the force (apparent force) on the body directed away from the center of rotation when the body is moving around a curve path. The same magnitude as Centripetal Force.

Example 3 A race car travels around the horizontal circular track that has a radius of 300 ft. If the car increases its speed at a constant rate of 7 ft/s2, starting from rest, a.) determine the time needed for it to reach an acceleration of 8 ft/s2. b.) What is its speed at this instant?

Example 4 A cyclist on a circular track of radius r=800ft is travelling 27 fps. His speed in the tangential direction increases at the rate of 3 fps2. What is the cyclists’ total acceleration.

Example 5 The model airplane has a mass of 0.90 kg and moves at constant speed on a circle that is parallel to the ground. The path of the airplane and the guideline lie in the same horizontal plane because the weight of the plane is balanced by the lift generated by its wings. Find the tension in the 17 m guideline for a speed of 19 m/s.

HS PHYS 001 GENERAL PHYSICS 1 Topic:

Two Dimensional Kinematics Written Work No. ____

Name : _______________________________________ Section: __________________________________ Date: __________________________

1. A stone is thrown horizontally at a speed of 5.0 m/s 4. Racing on a flat track, a car going 32 m/s rounds a from the top of a cliff 78.4 m high. curve 56 m in radius. What is the car’s centripetal a. How long does it take the stone to reach the acceleration? bottom of the cliff?

b. How far from the base of the cliff does the stone 5. A 615-kg racing car completes one lap in 14.3 s around hit the ground? a circular track with a radius of 50.0 m. The car moves at constant speed. What is the acceleration of the car?

c. What are the horizontal and vertical components of the stone’s velocity just before it hits the ground?

2. The player then kicks the ball with the same speed, but 6. An athlete whirls a 7.00-kg hammer tied to the end of at 60.0° from the horizontal. What are the ball’s hang a 1.3-m chain in a horizontal circle. The hammer makes time, range, and maximum height? one revolution in 1.0 s. What is the centripetal acceleration of the hammer?

3. A runner moving at a speed of 8.8 m/s rounds a bend 7. According to the Guinness Book of World Records with a radius of 25 m. What is the centripetal (1990) the highest rotary speed ever attained was acceleration of the runner? 2010 m/s (4500 mph). The rotating rod was 15.3 cm (6 in.) long. Assume that the speed quoted is that of the end of the rod. What is the centripetal acceleration of the end of the rod?

HS PHYS 001 GENERAL PHYSICS 1 Topic:

Forces and Newton’s Law of Motion Intended Learning Outcomes:

1. Restate Newton’s laws of motion. 2. Give illustrative examples for each laws. 3. Apply the 1st condition of equilibrium in Newton’s laws of motion. Concept of Force Force – an interaction that causes an acceleration of a body, can either be push or pull. This includes gravitational, electrostatic, magnetic and contact influences.

𝑭 = 𝒎𝒂 𝑭 = 𝐹𝑜𝑟𝑐𝑒, 𝑁𝑒𝑤𝑡𝑜𝑛, 𝑁 𝒎 = 𝑚𝑎𝑠𝑠, 𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚𝑠, 𝑘𝑔𝑠. 𝒂 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛, 𝑚/𝑠 2 Note: 1 𝑁 = 1 𝑘𝑔 𝑥

𝑚 𝑠2

Mass – amount of “stuff” contained in an object, a scalar quantity External forces (considered in engineering mechanics) are those actions of other bodies on a rigid body while those forces that hold together parts of a rigid body are called internal forces (considered in strength of materials, dependent on point of application ). Some particular forces include: 1. Weight (of a body) – the gravitational force that the earth exerts on the object. It always acts downward, towards the center of earth.

3. Frictional Force (Ff) – a force which opposes the motion of a body at rest or in motion. 4. Tensional Force (FT) – the force exerted by a string, rope or cable on an object to which it is attached, pulls the object in the direction of the rope 5. Applied Force (FA) – is a force that is applied to an object by a person or another body. 6. Air Resistance Force (FAIR) – Is a special type of frictional force that acts upon an object as they travel through the air. It opposes the motion of an object. Sometimes neglected. 7. Electrical Force (FE) – Attraction and repulsion of charges causes electrical force. 8. Magnetic Force (FM) – Attraction and repulsion of magnets causes magnetic force. Newton’s Law of Motion I. Newton’s First Law: The Law of Inertia “A body at rest, or in a state of motion with constant speed, has no acceleration, unless acted upon by an unbalanced force.” Consider:

𝑭𝒈 = 𝑾 = 𝒎𝒈 𝑾 = 𝑊𝑒𝑖𝑔ℎ𝑡, 𝑁 𝒎 = 𝑚𝑎𝑠𝑠, 𝑘𝑔𝑠. 𝒈 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛, 𝟗. 𝟖𝟏𝒎/𝒔𝟐 2. Normal Force (FN) – the perpendicular force (perpendicular to the surface) experienced by a body that is pressed against a surface.

At rest

In Motion

⃗⃗ = 𝟎, 𝒕𝒉𝒆𝒏 𝒂 = 𝟎. 𝑰𝒇 ∑𝑭 Inertia – the natural tendency of an object to remain at rest or in motion at a constant speed along a straight line

Free-Body Diagram – a sketch of the isolated body which shows only the forces acting upon the body. The forces acting on the free body are the action forces, also called applied forces. The reaction forces are those exerted by the free body upon other bodies. Example of a Free-Body Diagram

The net force (ΣF) is the vector sum of all the forces acting on an object.

II. Newton’s Second Law: The Law of Acceleration “Whenever a net (resultant) force acts on a body, it produces an acceleration in the direction of the resultant force that is directly proportional to the resultant force and inversely proportional to the mass of the body.”

Example 1 Two people are pushing a stalled car, as shown. The mass of the car is 1850 kg. One person applies a force of 275N to the car, while the other applies a force of 395N. A third force of 560N also acts on the car in the opposite direction. This force arises because of friction. Find the acceleration of the car.

If motion is along horizontal, ⃗⃗⃗⃗⃗𝒙 = 𝒎 · 𝒂 ⃗⃗𝒙 ∑𝑭 If motion is along horizontal, ⃗⃗⃗⃗⃗𝒚 = 𝒎 · 𝒂 ⃗⃗𝒚 ∑𝑭 Note: All the forces acting along the direction of motion is always (+), while the forces acting opposite the direction of motion is taken as (−).

_____________________________________________ _____________________________________________

III. Newton’s Third Law: The Law of Interaction

_____________________________________________

“For every action acting on an object, there is always an equal and opposite reaction.”

_____________________________________________ _____________________________________________

Example 2

Example 4

A hockey puck having a mass of 0.30 kg slides on the horizontal, frictionless surface of an ice rink. Two hockey sticks strike the puck simultaneously, exert-ing the forces on the puck shown in the figure. The force has a magnitude of 5.0 N, and the force has a magnitude of 8.0 N. Determine both the magnitude and the direction of the puck’s acceleration.

A 1580-kg car is traveling with a speed of 15.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 50.0 m? _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ Example 5 A student is skateboarding down a ramp that is 6.0 m long and inclined at 18o with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 2.6 m/s. Neglect friction and find the speed at the bottom of the ramp.

_____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ Example 3 Suppose that the magnitude of the force is 36 N. If the mass of the spacecraft is 11,000 kg and the mass of the astronaut is 92 kg, what are the accelerations?

_____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ Example 6 A 95.0-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.80 m/s2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.80 m/s2?

_____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________

_____________________________________________ _____________________________________________

_____________________________________________ _____________________________________________ _____________________________________________ Example 7 An Atwood machine is a device used at laboratories to calculate the value of 𝑔. Two objects with mass 7.0 kg and 5.0 kg are suspended at the end of the cord that passes over a massless frictionless pulley as shown. a.) What is the acceleration of the system? b.) What is the tension in the cord?

𝑭𝒇 = 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒, 𝑁 𝝁 = 𝑚𝑢, 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 0 < 𝜇 < 1, 𝑢𝑛𝑖𝑡𝑙𝑒𝑠𝑠 𝑵 = 𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒, 𝑁

Static Friction – opposes the impending relative motion between to objects 𝑭𝒔 = 𝝁𝒔 · 𝑵 Kinetic Friction – exists when an object does not slide along a surface on which it rests even though a force is exerted to make it slide 𝑭𝒌 = 𝝁𝒌 · 𝑵 Generally, 𝒇𝒔 > 𝒇𝒌 _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________

Frictional Force First Condition of Equilibrium Friction – produced when a body is rubbing over a surface. It opposes the motion of an object directed parallel to the The vector sum of all the forces acting on the body is zero. surface of contact. An object has zero acceleration.

Collinear Forces – forces acting on the same line of action Concurrent Forces – forces acting at the same point

Coplanar Forces – forces acting along the same plane Equilibrant – single force applied at the same point that produces equilibrium Note:

_____________________________________________ _____________________________________________ _____________________________________________

When an object is accelerating, it is not in equilibrium. Example 3 Therefore, Newton’s second law of acceleration is applied. A 250 𝑙𝑏. block is initially at rest on a flat surface that is inclined at 30°. If the coefficient of kinetic friction and static friction is 0.30 and 0.40, respectively, find the force required to start the block moving up the plane. Example 1 _____________________________________________ A traffic light weighing 122 N hangs from a cable tied to _____________________________________________ two other cables fastened to a support as shown. The upper cables make angles of 37.0° and 53.0° with the _____________________________________________ horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds _____________________________________________ 100 N. Does the traffic light remain hanging in this _____________________________________________ situation, or will one of the cables break? Example 4 A block weighing 200N rests on a plane inclined upward to the right at a slope of 4 vertical to 3 horizontal. The block is connected by a cable initially parallel to the plane passing through a pulley which is connected to another block weighing 100N moving vertically. The coefficient of kinetic friction between the 200N block and the inclined plane is 0.10. Which of the following most nearly gives the acceleration of the system. _____________________________________________ _____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________

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Example 2

Example 5

What is the magnitude and direction of the single force applied to make the two concurrent forces (86.60 𝑁, 𝑁 30° 𝐸 and 70.7 𝑁, 𝑁 45° 𝑊) in equilibrium?

A hockey puck on a frozen pond is given an initial speed of 20.0 m/s. If the puck always remains on the ice and slides 115 m before coming to rest, determine the coefficient of kinetic friction between the puck and ice.

_____________________________________________ _____________________________________________

HS PHYS 001 GENERAL PHYSICS 1 Topic:

Forces and Newton’s Law of Motion Written Work No. ____

Name : _______________________________________ Section: __________________________________ Date: __________________________

Choose the letter of the correct answer. Shade the letter, that corresponds to your answer, Provide your solution at the back of the paper.

(2) the force of the table pushing on the book (3) the force of the book pushing on the table (4) the force of the book pulling on the earth

1.

With one exception, each of the following units can be used to express mass. What is the exception? a. Newton c. kilogram b. gram d. slug

7.

Which two forces form an "action-reaction" pair that obeys Newton's third law? a. 1 and 2 c. 3 and 4 b. 1 and 4 d. 1 and 3

2.

Complete the following statement: The term net force most accurately describes a. the mass of an object b. the inertia of an object. moving. c. the quantity that causes displacement. d. the quantity that changes the velocity of an object.

8.

The book has an acceleration of 0 m/s2. Which pair of forces, excluding "action-reaction" pairs, must be equal in magnitude and opposite in direction? a. 1 and 2 c. 2 and 4 b. 1 and 4 d. 1 and 3

3.

Which one of the following terms is used to indicate the natural tendency of an object to remain at rest or in motion at a constant speed along a straight line? a. Velocity c. inertia b. acceleration d. force

4.

When the net force that acts on a hockey puck is 10 N, the puck accelerates at a rate of 50 m/s2. Determine the mass of the puck. a. 0.2 kg c. 50 kg b. 5 kg d. 1.0 kg

For items 5-6. A horse pulls a cart along a flat road. Consider the following four forces that arise in this situation. (1) the force of the horse pulling on the cart (2) the force of the cart pulling on the horse (3) the force of the horse pushing on the road (4) the force of the road pushing on the horse 5.

Which two forces form an "action-reaction" pair that obeys Newton's third law? a. 1 and 4 c. 2 and 3 b. 2 and 4 d. 3 and 4

6.

Suppose that the horse and cart have started from rest; and as time goes on, their speed increases in the same direction. Which one of the following conclusions is correct concerning the magnitudes of the forces mentioned above? a. Force 1 exceeds force 2. b. Force 3 exceeds force 4. c. Force 2 is less than force 3. d. Forces 1 and 2 cannot have equal

For items 7-8. A book is resting on the surface of a table. Consider the following four forces that arise in this situation: (1) the force of the earth pulling on the book

For items 9-10. A 2.0-N force acts horizontally on a 10-N block that is initially at rest on a horizontal surface. The coefficient of static friction between the block and the surface is 0.50. 9.

What is the magnitude of the frictional force that acts on the block? a. 0 N c. 10 N b. 5 N d. 2 N

10. Suppose that the block now moves across the surface with constant speed under the action of a horizontal 3.0-N force. Which statement concerning this situation is not true? a. The block is not accelerated. b. The net force on the block is zero Newton. c. The frictional force on the block has magnitude 3.0 N. d. The direction of the total force that the surface exerts on the block is vertically upward.