• Author / Uploaded
• Ahmad Shah

• Categories
• Impulso
• Momento angular
• Energía cinética
• Fuerza
• Velocidad

Citation preview

Assoc. Prof. Raafat Ibrahim

1

2

ENERGY

(joules)

3

Conservation of ENERGY IF, •In a mass system where internal friction forces are sufficiently small to be neglected

AND •No work is done on the system during an interval of motion by external force (other than gravitational force)

THEN The net energy of the system remains constant

That is, 4

Conservation of ENERGY The net energy of the system remains constant

That is,

5

EXAMPLE 1 The 3kg slider is released from rest at position 1 and slides with negligible friction in a vertical plane along the circular rod. The attached spring has a stiffness of 350 N/m and has an unstretched length of 0.6m. Determine the velocity of the slider as it passes position 2.

6

EXAMPLE 1 The 3kg slider is released from rest at position 1 and slides with negligible friction in a vertical plane along the circular rod. The attached spring has a stiffness of 350 N/m and has an unstretched length of 0.6m. Determine the velocity of the slider as it passes position 2.

7

EXAMPLE 1 The 3kg slider is released from rest at position 1 and slides with negligible friction in a vertical plane along the circular rod. The attached spring has a stiffness of 350 N/m and has an unstretched length of 0.6m. Determine the velocity of the slider as it passes position 2. Substituting in conservation of energy equation

8

Linear momentum of a system of particles • Linear momentum (G) = mv

Cm

For a particle of mass system

of the

Linear momentum of the system is the vector sum of the linear momenta of all its particles (1) 9

Linear momentum of a system of particles Velocity of mass

w.r.t O

Substituting in Eq. (1)

velocity of center of mass velocity of w.r.t translating reference frame moving with Cm

Cm

From the definition of center of mass

Therefore,

10

Linear Impulse-Momentum principle

Product of force and time – Linear Impulse

Total external linear impulse (impact force) on the particle equals the corresponding change in the linear momentum 11

EXAMPLE 2

z

F

mg

y 12

Angular momentum of a system of particles

Cm

13

Angular momentum of a system of particles

Cm

14

Angular momentum of a system of particles

Cm

15

Angular Impulse-Momentum

16

EXAMPLE 3

17

Conservation of Momentum In the absence of an external impulse, the momentum of a system remains unchanged

18

EXAMPLE 4 The 25Mg flatcar supports a 7.5Mg vehicle on a 5o ramp built on the flatcar. If the vehicle is released from rest with the flat car also at rest, determine the velocity v of the flatcar when the vehicle has rolled s =12m down the ramp just before hitting the stop at B. Neglect all friction and treat the flatcar as particles.

v

5o

x s

y 19

EXAMPLE 4

5o

v

x

s

y 20

EXAMPLE 4

5o

v

x s

y

21

EXAMPLE 4

5o

v

x s

y

22

What You Learned! • Work and Energy – Conservation of Energy

• Impulse and Momentum – Linear Impulse and Momentum – Angular Impulse and Momentum – Conservation of Momentum