Name: ______

Chapter 13, 14 & 16 Review

1. Oscillating Spring

A. Starting from Hooke’s Law, show the steps to get to the SHM differential equation for an oscillating spring.

B. What is the angular frequency and period?

2. Oscillating Physical Pendulum

A. Starting from the equation for torque, show the steps to get to the SHM differential equation for an oscillating rod (ICM = ML2), where the pivot point is a distance b from the center of mass. (Hint: You will need to equate the two expressions for torque.)

B. What is the angular frequency and period?

3. A uniform bar of length L = 3.00m and a weight of 200 N is suspended by a wire that can withstand a maximum tension of 500 N and makes an angle with respect to the bar of  = 30.0o. A block that weighs 300 N rests on rest on the bar a distance x from the wall as shown.

A. What is the maximum possible distance x before the wire breaks?

B. With the block placed at this maximum x, what are the horizontal and vertical components of the force on the bar from the hinge at A?

4. A climber leans out against a vertical ice wall that has negligible friction. Distance a is 0.914 m and distance L is 2.10 m. His center of mass is distance d = 0.940 m from the feet–ground contact point. If he is on the verge of sliding, what is the coefficient of static friction between feet and ground?

5. A spherical hollow “resides” inside a lead sphere of radius R = 4.00 cm. The“surface” of the hollow passes through the center of the sphere and “touches” the right side of the sphere. The mass of the sphere before hollowing was M = 2.95 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 0.431 kg that lies at a distance d = 9.00 cm from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow? [Hint: Find the force if the sphere was solid. Then find the force from the hollow portion if it were filled. Subtract the two.]

6. A spherical asteroid has a radius of 500 km. The gravitational acceleration at its surface is 3.0 m/s2.

A. What is the escape speed from the surface of the asteroid?

B. How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

C. With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?

Solutions:

1. A.

B.

2. A. where I = ML2 + mb2

B.

3. A. 1.50 m

B. Fx = 433 NFy = 250 N

4. 0.216

5. 8.31 x 10-9 N

6. A. 1.7 x 103 m/s

B. 2.5 x 105 m

C. 1.4 x 103 m/s