Problem Set 3

Reading for this week includes Chapter 4 and sections 5-1 through 5-5. It is best to read the chapter before the class and re-read it afterwards. On a trial basis I have included the statement of all the problems.

(1) Ch 3 P 31 Solve this without using the numbers, although you can check your results with the numbers given: A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37.0º with the horizontal, as shown in Fig. 3–35. (a) Determine the time taken by the projectile to hit point P at ground level. (b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find (c) the horizontal and the vertical components of its velocity, (d) the magnitude of the velocity, and (e) the angle made by the velocity vector with the horizontal. (f) Find the maximum height above the cliff top reached by the projectile.

(2) Ch 4 P 49 A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?

(3) 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

(4) 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?

(5) Consider the experiments in (4) but now with the car uniformly accelerating in the forward direction

(6) Consider the two-mass and pulley example we discussed in class on Wednesday, Septemeber 12. As we did in class, find the acceleration but now suppose the tabletop is not frictionless.

(7) A crate with mass 46.3 kg is pushed up a frictionless incline (angled 20.0º up from horizontal) with a constant horizontal force. The magnitude of the acceleration is 0.100 m/s^2. (a) Find the magnitude and direction of the applied force. (b) What is the weight of the crate? (c) What is the magnitude of the normal force?

(8) Ch 4 P 52 The carton shown in Fig. 4–55 lies on a plane tilted at an angle theta=22.0º to the horizontal, with the coef,. of friction of 0.12 (a) Determine the acceleration of the carton as it slides down the plane. (b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton’s speed when it reaches the bottom of the incline?

(9) Ch 4 P 75 Francesca, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4–58). She notices that the string makes an angle of 25º with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s. Estimate the takeoff speed of the aircraft.

(10) Ch 4 P 77 In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N. Ignoring friction, at what maximum angle theta should the ramps be built, assuming a full 30-kg grocery cart?