## Phys 100: Problem Set Week 4

Due Wednesday September 26, at 9 AM

### Reading:

We will finish our discussion of Giancoli Chapter 4 (Dynamics) and start on Chapter 5 (circular motion and gravitation). The problems are on kinematics in 2+1 and on dynamics.

### Problems:

(1) Suppose you are sitting on a chair that stands on the ground. Carefully draw force diagrams of your body, the chair, and the whole earth. Describe each force in words. Identify third law "equal and opposite force" pairs.

(2) A railroad car moves with constant velocity along a track. Observer Alice performs experiments inside the car while Observer Bob, outside the car at a fixed location along the track, watches these experiments as Alice moves by. In each of the following experiments, describe what the observers see in their own reference frame. Include sketches of the trajectories.
(i) Alice puts a ball on the level floor of the car. Will it stay where she places it?
(ii) Alice rolls the ball along the floor in a straight line towards the front of the car.
(iii) Alice drops the ball onto the floor.
(iv) Alice suspends the ball from the ceiling of the car with some string, making a pendulum.
(v) Alice fills an aquarium, resting on the floor, with water. How does the surface of the water behave?

(3) Consider the experiments in (2) but now with the car uniformly accelerating in the forward direction.

(4) Ch 4 Question 9

(5) Perform the analysis of the demo from Wednesday September 19 to show whether the ball will hit the target.

(6) Ch 3 Problem 20

(7) Ch 3 Problem 31

(8) Ch 3 Problem 35

(9) An apple sits upon the head of an unfortunate offspring of William Tell, who stands 27.0 m away and launches his arrows at a speed of 35.0 m/s. Suppose William Tell has an angular uncertainty of 0.1 degree. What happens if his launch angle is off by this much? Assume that the arrow's launch point is the same height as the center of the apple and that the apple has a height of 9.00 cm.

(10) You pull a sled, with mass m, at a constant speed and along a horizontal snowy surface such that the rope makes an angle "theta" with the horizontal . The coefficient of friction between the snow and the sled is "mu". Draw the force diagrams for the sled and you. Calculate the tension in the rope.