Physics 201 MWF10:20 Fall 1996 (Ford)
Exam III Chapts. 9,10,11,13 in SZY College Physics

Show all your work. Partial credit will be given if earned. Write your answers in the blanks provided.


(18 pts) 1. A block on a horizontal frictionless surface is attached to a spring and put into simple harmonic motion with amplitude 0.20 m. When the block is 0.10 m to the left of its equilibrium position its acceleration is 5.0 m/s².

a) What is the magnitude of the velocity of the block at this instant?

Ans. ___1.22 m/s___

b) What is the magnitude of the maximum velocity of the block?

Ans. ___1.41 m/s___

c) What is the frequency f (in Hz) of the motion?

Ans. ___1.13 Hz___


(18 pts) 2. When a solid brass statue is suspended in air from a light rope the tension in the rope is 60 N. The statue is then totally immersed in water. The density of brass is 8600 kg/m³ and the density of water is 1000 kg/m³.

a) What is the volume of the statue?

Ans. ___7.12×10^-4 m³___

b) What is the tension in the rope when the statue is totally immersed in water?

Ans. ___53.0 N___


(22 pts) 3. A uniform ladder 12 m long rests against a vertical frictionless wall. The ladder weighs 450 N and makes an angle of 30° with the wall. There is friction between the ladder and the floor. A man weighing 700 N climbs slowly up the ladder. When he passes the point 11 m along the ladder from the bottom, the ladder starts to slip.

a) When the man is 11 m from the bottom of the ladder, what is the normal force exerted by the floor on the ladder?

Ans. ___1150 N___

b) When the man is at this position along the ladder, what is the normal force exerted by the wall on the ladder?

Ans. ___500 N___

c) What is µ_s, the coefficient of static friction between the floor and the ladder?

Ans. ___0.435___


(22 pts) 4. A horizontal disk with radius R = 0.4 m and mass M = 1.4 kg is pivoted about a vertical axis through its center. The disk is initially at rest. A small bullet with mass 0.1 kg is fired with speed v₀ toward the rim of the disk. The bullet strikes the rim of the disk and sticks. After the bullet strikes, the disk turns with an angular velocity of 3 rad/s.

a) What is the moment of inertia I of the disk with the bullet stuck to its rim, for a vertical axis through the center of the disk?

Ans. ___0.128 kg·m²___

b) What is the initial angular momentum of the bullet, before it strikes the disk, for a vertical axis through the center of the disk?

Ans. ___0.384 kg·m²·s^-1___

c) What is the initial speed of the bullet, before it strikes the disk?

Ans. ___9.6 m/s___


(20 pts) 5. A cylinder with radius R = 0.18 m is pivoted on frictionless bearings about an axis through its center. A rope is wrapped around the cylinder, and a block with mass m = 2.0 kg is suspended from the free end of the rope. The block is initially 4.0 m above the floor. The system is released from rest and the block has speed 5.0 m/s just before it hits the floor.

a) Just before the block hits the floor, what is the angular velocity of the cylinder?

Ans. ___27.8 rad/s___

b) Just before the block hits the floor, what is the kinetic energy of the cylinder?

Ans. ___53.4 J___