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# A weight of 50.025 m and a mass 3.

3. A weight of 50.0 N is attached to the free end of a light string wrapped around a pulley of radius 0.025 m and a mass 3.0 kg. The pulley is free to rotate in a vertical plane about the horizontal axis passing through its center. The weight is released 6.0 m above the floor. (a) Determine the tension in the string, the acceleration of the mass, and the speed with which the weight hits the floor. (b) Find the speed calculated in part (a) by using the principle of conservation of energy. (11.37 N, 7.58 m/s2, 9.54 m/s, 9.54 m/s)

4. Find the net torque on the wheel shown in the figure about the axle through 0 if a =10 cm and b =25 cm. (-3.71 N.m, going into paper)
5. The blocks shown in the figure are connected by a string of negligible mass passing over a pulley of radius R=0.25 m and moment of inertia I. The block on the incline is moving up with a constant acceleration of magnitude a= 2.0 m/s2 (a) Determine T1 and T2, the tension in the two parts of the string, and (b) find the moment of inertia of the pulley. (118.5 N, 156 N, 1.17 kg.m2)

6. A ladder of weight 400 N and length 10.0 m is placed against a smooth vertical ' wall. A person weighing 800 N stands on the ladder 2.0 m from the bottom as measured along the ladder. The foot of the ladder is 8.0 m from the bottom of the wall. Calculate the force exerted by the wall, and the normal force exerted by the floor on the ladder. (480 N, 1200 N)
7. A 1500 kg.-automobile has a wheel base (the distance from the axles) of 3 m. The center of mass of the automobile is on the center line at a point 1.2 m behind the front axle. Find the force exerted by the ground on each wheel. (4410 N).
8. A 200 kg. Load is hung on a wire of length 4.0 m, cross-sectional area 0.2 cm2, and Young's modulus 8.0x1010 N/m2. What is its increase in length? (4.9 mm)
9. When water freezes, it expands about 9%. What would be the pressure increase inside your automobile engine block if the water in it freezes? (The bulk modulus of ice is 2.0x109 N/m2) (1.8x108 N/m2)

10. The step ladder of negligible weight is constructed as shown in the figure. A painter of mass 70.0 kg stands on the ladder 3.0 m from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar connecting the two halves of the ladder. (b) The normal forces at A and B, (c) the components of the reaction force at the hinge C that the left half of the ladder exerts on the right half.
(133 N, 429 N, 257 N, 133 N, 257 N)
11. The displacement of a particle at any time t is given by the expression x = 4cos (3t+), where x is in meters and t is in seconds. Determine (a) the frequency and period of motion (b) the amplitude of the motion (c) the phase constant, and (d) the displacement of the particle at t =0.25 s. (0.48 Hz, 4 m,  rad, -2.93m)
12. A particle moving along the x-axis in simple harmonic motion starts from the origin at 1=0 and moves to the right. If the amplitude of its motion is 2.0 cm and the frequency is 1.5 Hz, (a) show-that its displacement is given by x = (2 cm) sin (3t). Determine (b) the maximum speed and the earliest time at which the particle has this speed, (c) the maximum acceleration and the earliest time at which the particle has this acceleration, and (d) the total distance traveled between t=0 and t=1. (1/3 s, .1.78 m/s2, 12 cm)
13. A 0.5 kg mass attached to a spring of force constant 8.0 N/m vibrating in simple harmonic motion with an amplitude of 10 cm. Calculate (a) the maximum value of its speed and acceleration, (b) the speed and acceleration when the mass is 6.0 cm from the equilibrium position, and (c) the time it takes the mass to move from x=0 to x=8.0 cm. (40 cm/s, 160 cm/ s2, 32 cm/s,-96 cm/s2, 0.23 s)

14. A particle executes simple harmonic motion with amplitude of 3.0 cm. At what displacement from the midpoint of
its motion does its speed equal one half of its maximum speed? (2.6 cm)

15 A centrifuge in a medical laboratory rotates at an angular speed of 3600 rev/min. When switched off, it rotates 50.0 times before coming to rest. Find the constant angular acceleration of the centrifuge. (-2.26×102 rad/s)

16 A rotating wheel requires 3.00 s to rotate through 37.0 revolutions Its angular speed at the end of 3.00 s interval is 98.0 rad/s. What is the constant angular acceleration of the wheel? (13.7 rad/s2)

17 A racing car travels on a circular track of radius 250 m. If the car moves with a constant linear speed of 45.0 m/s, find (a) its angular speed and (b) the magnitude and direction of its acceleration. (0.180 rad/s, 8.10 m/s2 to center)

18 A car accelerates uniformly from rest and reaches a speed of 22.0 m/s in 9.00 s. If the diameter of the tire is 58.0 cm, find (a) the number of revolutions the tire makes during the motion, assuming that no slipping occurs. (b) What is the final angular speed of a tire in revolutions per second? (54.3 rev, 12.1 rev/s)

19 A grinding wheel is in the form of a uniform solid disc of radius 7.00 cm and mass 2.00 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.600 N.m that the motor exerts on the wheel . (a) How long does the wheel take to reach its final operating speed of 1200 rev/min? (b) Through how many revolutions does it turn while accelerating? (1.03 s, 10.3 rev)

20 A cylinder of mass 10.0 kg rolls without slipping on a horizontal surface. At the instant its center of mass has a speed of 10.0 m/s, determine (a) the translational kinetic energy of its center of mass, (b) the rotational kinetic energy about its center of mass, and (c) its total energy. (500 J, 250 J, 750 J)

21. A car traveling on a flat (unbanked) circular track accelerates uniformly from rest with a tangential acceleration of 1.70 m/s2. The car makes it one quarter of the way around the circle before it skids off the track. Determine the coefficient of static friction between the car and track from these data. (0.572)

22. An object with a weight of 50.0 N is attached to the free end of a light string wrapped around a reel of radius 0.250 m and mass 3.00 kg. The reel is a solid disc, free to rotate in a vertical plane about the horizontal axis passing through its center. The suspended object is released 6.00 m above the floor. (a0 Determine the tension in the string, the acceleration of the object, and the speed with which the object hits the floor. (b0 Verify your last answer by using the principle of conservation of energy to find the speed with which the object hits the floor. (9.5 m/s)

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