PHYSICS 150 Homework (Fall 2015) Varriano

1. (Rotational Motion with Uniform Acceleration) You hop into your car and speed away from CBU. Assuming that you accelerate uniformly from rest at t=0 to a speed of 15 m/s in 5 seconds and that the diameters of your tires are 60 cm, answer the following questions:

(a) What is the angular acceleration of one of your tires? (b) What is the angular speed of this tire at t=5 s? (c) How many revolutions does one of your tires make during this time? (d) If a stone is caught in the tread of this tire, what is the tangential acceleration of the stone? (e) What is the radial (centripetal) acceleration of this stone at t=5 s?

ANSWERS: (a) 10 rad/s2 (b) 50 rad/s (c) 19.9 revs (d) 3 m/s2 (e) 750 m/s2

2.(Static Equillibrium) A 2500-gram board, 140 cm in length, is placed on a fulcrum. The mass of the board is uniformly distributed. When a 300-gram block is placed 30 cm to the right of the fulcrum, the board is balanced on the fulcrum.

(a) On what side of the fulcrum must be the board's center of mass? (b) How far from the fulcrum is the board’s center of mass? (c) What is the size of the force exerted by the fulcrum on the board? (d) Suppose the block is removed. To balance the board, you push down on one end of the board. How hard do you have to push? ANSWERS: (a) Tell me. (b) 3.6 cm (c) 27.4 N (d) 1.33 N

3. (The Rolling Yo-Yo) A yo-yo has an inner radius of 0.5 cm, an outer radius of 3 cm, a mass of Orientation 1 0.5 kg, and a moment of inertia of 1.85 kg cm2 about an axis through its center. We saw in class that the yo-yo will roll to the right regardless of whether the string comes off of the top of the axle (Orientation 1) or the bottom of the axle (Orientation 2). Orientation 2 (a) If you pull on the string in Orientation 1, find the tension needed to provide an acceleration of 20 cm/s2 to the right. (b) If you pull on the string in Orientation 2, find the tension needed to provide the same acceleration to the right.

ANSWERS: (a) 0.121 N (b) 0.169 N 4. (Simple Harmonic Oscillator) A 500-gram object is attached to a spring with a spring constant of 250 N/m. The mass reaches a maximum distance of 3.5 cm from its equilibrium position.

(a) The position of the object can be written as x(t) = A cos(ωt). Find the values of A and ω. (b) Find the time it takes for the object to complete one oscillation. (c) Find the total energy of the object. (d) Find the maximum speed of the object. At what position does this occur? (e) Find the maximum acceleration of the object. At what position does this occur?

ANSWERS: (a) You tell me. (b) 0.28 seconds (c) 0.153 J (d) 0.783 m/s at x=0 (e) 17.5 m/s2 at x=±3.5 cm