• Author / Uploaded
• Ardila Daniel

• Categories
• Fuerza
• Esfuerzo de torsión
• Movimiento (Física)
• Física aplicada e interdisciplinaria
• Aceleración

Citation preview

412  Chapter

6  Plane Ki net i c s of Ri gi d Bodi es

PROBLEMS

friction is limited to 0.25 between the wheels and the rail. Neglect the small mass of the wheels.

Introductory Problems 6/1 The right-angle bar with equal legs weighs 6 lb and is freely hinged to the vertical plate at C. The bar is prevented from rotating by the two pegs A and B fixed to the plate. Determine the acceleration a of the plate for which no force is exerted on the bar by either peg A or B. 8″ Problem 6/4

6/5 The uniform box of mass m slides down the rough incline. Determine the location d of the effective normal force N. The effective normal force is located at the centroid of the nonuniform pressure distribution which the incline exerts on the bottom surface of the block.

C a

8″ A

B

v

b h

Problem 6/1 G

m

6/2 In Prob. 6 /1, if the plate is given a horizontal acceleration a = 2g, calculate the force exerted on the bar by either peg A or B. 6/3 The driver of a pickup truck accelerates from rest to a speed of 45 mi / hr over a horizontal distance of 225 ft with constant acceleration. The truck is hauling an empty 500-lb trailer with a uniform 60-lb gate hinged at O and held in the slightly tilted position by two pegs, one on each side of the trailer frame at A. Determine the maximum shearing force developed in each of the two pegs during the acceleration.

μk N

θ

d Problem 6/5

6/6 The uniform slender bar of mass m and length L is held in the position shown by the stop at A. What acceleration a will cause the normal force acting on the roller at B to become (a) one-half of the static value, (b) one-fourth of the static value, and (c) zero?

3° B 48″ L

A 10″ O

A

m

a

θ

Problem 6/3

Problem 6/6

6/4 A passenger car of an overhead monorail system is driven by one of its two small wheels A or B. Select the one for which the car can be given the greater acceleration without slipping the driving wheel and compute the maximum acceleration if the effective coefficient of

6/7 The homogeneous crate of mass m is mounted on small wheels as shown. Determine the maximum force P which can be applied without overturning the crate about (a) its lower front edge with h = b and (b) its lower back edge with h = 0.

A rt i c l e 6 / 3     P r o b l e ms   413

c

and that of the cart is M. The cart wheels have negligible mass and friction.

P m

b

h

G r/2

B

r/2

P

A

M Problem 6/7

6/8 The frame is made from uniform rod which has a mass  per unit length. A smooth recessed slot constrains the small rollers at A and B to travel horizontally. Force P is applied to the frame through a cable attached to an adjustable collar C. Determine the magnitudes and directions of the normal forces which act on the rollers if (a) h = 0.3L, (b) h = 0.5L, and (c) h = 0.9L. Evaluate your results for  = 2 kg/m, L = 500 mm, and P = 60 N. What is the acceleration of the frame in each case?

Problem 6/10

6/11 The uniform 5-kg bar AB is suspended in a vertical position from an accelerating vehicle and restrained by the wire BC. If the acceleration is a = 0.6g, determine the tension T in the wire and the magnitude of the total force supported by the pin at A.

L C L

P h

A

B Problem 6/8

6/9 A uniform slender rod rests on a car seat as shown. Determine the deceleration a for which the rod will begin to tip forward. Assume that friction at B is sufficient to prevent slipping.

Problem 6/11

6/12 If the collar P is given a constant acceleration a = 3g to the right, the pendulum will assume a steadystate deflection  = 30°. Determine the stiffness kT of the torsional spring which will allow this to happen. The torsional spring is undeformed when the pendulum is in the vertical position. a P kT m L

Problem 6/9

θ

6/10 Determine the value of P which will cause the homogeneous cylinder to begin to roll up out of its rectangular recess. The mass of the cylinder is m

m Problem 6/12

A rt i c l e 6 / 4     P r o b l e ms   421

PROBLEMS

4″

O

Introductory Problems

B

6/33 Two pulleys are fastened together to form an integral unit. At a certain instant, the indicated belt tensions act on the unit and the unit is turning counterclockwise. Determine the angular acceleration of the unit for this instant if the moment due to friction in the bearing at O is 2.5 N ∙ m.

m = 25 kg kO = 250 mm

500 mm

A 6″

48″ Problem 6/35

6/36 The uniform 100-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with ␪ = 0. Determine the initial angular acceleration ␣ of the beam and the magnitude FA of the force supported by the pin at A due to the application of the force P = 300 N on the attached cable.

1400 N

1150 N

3m

650 N O 45°

14″

A

300 mm

C

475 N

P 3m

θ

Problem 6/33

6/34 The uniform 20-kg slender bar is pivoted at O and swings freely in the vertical plane. If the bar is released from rest in the horizontal position, calculate the initial value of the force R exerted by the bearing on the bar an instant after release.

O

1.6 m Problem 6/34

6/35 The figure shows an overhead view of a hydraulicallyoperated gate. As fluid enters the piston side of the cylinder near A, the rod at B extends causing the gate to rotate about a vertical axis through O. For a 2-in.-diameter piston, what fluid pressure p will give the gate an initial counterclockwise angular acceleration of 4 rad /sec? The radius of gyration about O for the 500-lb gate is kO = 38 in.

1m

B Problem 6/36

6/37 The motor M is used to hoist the 12,000-lb stadium panel (centroidal radius of gyration k = 6.5 ft) into position by pivoting the panel about its corner A. If the motor is capable of producing 5000 lb-ft of torque, what pulley diameter d will give the panel an initial counterclockwise angular acceleration of 1.5 deg /sec2? Neglect all friction.

15°

M

d

10′ A

Problem 6/37

20′

B

422  Chapter

6  Plane Ki net i c s of Ri gi d Bodi es

6/38 A momentum wheel for dynamics-class demonstrations is shown. It is basically a bicycle wheel modified with rim band-weighting, handles, and a pulley for cord startup. The heavy rim band causes the radius of gyration of the 7-lb wheel to be 11 in. If a steady 10-lb pull T is applied to the cord, determine the angular acceleration of the wheel. Neglect bearing friction. 24″

T = 10 lb

r

r O

O

C

C

(b)

(a) Problem 6/40

30° 4″

6/41 The uniform 5-kg portion of a circular hoop is released from rest while in the position shown where the torsional spring of stiffness kT = 15 N ∙ m /rad has been twisted 90° clockwise from its undeformed position. Determine the magnitude of the pin force at O at the instant of release. Motion takes place in a vertical plane and the hoop radius is r = 150 mm. kT O

Problem 6/38

6/39 Each of the two drums and connected hubs of 8-in. radius weighs 200 lb and has a radius of gyration about its center of 15 in. Calculate the angular acceleration of each drum. Friction in each bearing is negligible.

8″

r

8″

Problem 6/41

6/42 The 30-in. slender bar weighs 20 lb and is mounted on a vertical shaft at O. If a torque M = 100 lb-in. is applied to the bar through its shaft, calculate the horizontal force R on the bearing as the bar starts to rotate.

30 lb (a)

30 lb

12″

(b) Problem 6/39

6/40 Determine the angular acceleration and the force on the bearing at O for (a) the narrow ring of mass m and (b) the flat circular disk of mass m immediately after each is released from rest in the vertical plane with OC horizontal.

18″

O

M

Problem 6/42