Chapter: Work, Energy & Momentum

1 (a) If you push against the wall of a building, are you doing any work? Explain.

(b) A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25° downward from the horizontal. Find the work done by the shopper as she moves down a 50-m length of aisle.

2 A 98.0-N grocery cart is pushed 12.0 m by a shopper who exerts a constant horizontal force of 40.0 N. If all frictional forces are neglected and the cart starts from rest, what is its final speed?

3 A student could either pull or push, at an angle of from the horizontal, a 50-kg crate on a horizontal surface, where the coefficient of kinetic friction between the crate and surface is 0.20. The crate is to be moved a horizontal distance of 15 m. Compared with pushing, pulling requires the student to do (1) less, (2) the same, or (3) more work

4 A roller coaster travels on a frictionless track as shown in figure below. (a) If the speed of the roller coaster at point A is what is its speed at point B? (b) Will it reach point C? (c) What speed at point *A* is required for the roller coaster to reach point *C*? (11m/s)

5 A pendulum is launched from a point of height *h* above its lowest point in two different ways as shown in figure above. During both launches, the pendulum is given an initial speed of 2.0 m/s. On the first launch, the initial velocity of the pendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause it to swing the largest angle from the equilibrium position? Give reason for your answer.

6 The graph shows how the force F on a body of mass 0.5kg varies with the displacement x form origin.

a. What is the work done by the force when the body is displaced 4.0m from the origin?

b. The velocity of the body at the origin is 2.0m/s. what is the velocity when it is 4.0m form the origin?

7 The total resistive force on a car travelling at a constant velocity of 20m/s is 1.6 x 10^{3}N. What is the minimum power of the car?

8 An electric motor of power 1200W is used to raise a load of 56 kg. Calculate the minimum time taken to raise the load through a distance of 8 m.

9 A puck glides on smooth surfaces when pushed or hit as in ice hockey. Benjamin is playing with a small puck on a smooth floor. The puck floats on a cushion of air above the floor so the effects of friction can be ignored. The puck has a mass of 155 g. Benjamin pushes the puck so it collides with a wall as shown below.

The puck hits the wall at a speed of 0.75 m s ^{−}^{1} and rebounds at a speed of 0.61 m s ^{−}^{1}. The collision lasts 0.065 s.

(a) Calculate the size of the momentum of the puck before it collides with the wall.

(b) An inelastic collision is one in which the kinetic energy before the collision is not the same as the kinetic energy after the collision. By doing suitable calculations show that the collision of the puck and the wall is inelastic.

(c) State where the “lost” energy has gone to.

(d) Determine the change in the puck’s momentum during the collision

(e) Calculate the size and direction of the average force the wall exerts on the puck.

(f) Determine the size and direction of the average force the puck exerts on the wall.

10 Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which stops it.

(a) Assuming there is no splashing back,

(i) what is the force exerted by the water on the car?

(b) What if the water splashes back from the car? Would the force on the car be greater or less?

11 A child in a boat throws a 5.4 kg package out horizontally with a speed of 10 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26 kg and that of the boat is 55.0 kg.

12 State the quantities that are conserved in an a) elastic collision b) inelastic collision

What happens to the quantity that is not conserved in one of the above collisions? How would you know that the collision between two particles moving with the same speed is perfectly elastic?

13 A pitcher throws a 0.15-kg baseball so that it crosses home plate horizontally with a speed of 20 m/s. It is hit straight back at the pitcher with a final speed of 22 m/s. (a) What is the impulse delivered to the ball? (b) Find the average force exerted by the bat on the ball if the two are in contact for 2.0 x 10^{–3} s.(6.3 Ns, 3.2 x 10^{3} N)

14 Two balls with masses of 2.0 kg and 6.0 kg travel toward each other at speeds of and , respectively. If the balls have a head-on, inelastic collision and the 2.0-kg ball recoils with a speed of how much kinetic energy is lost in the collision? (1.1 x 10^{2} J)

15 A 25.0-g object moving to the right at 20.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.

16 A bullet of mass 2.0 g is fired horizontally into a block of wood of mass 600 g. The block is suspended from strings so that it is free to move in a vertical plane. The bullet buries itself in the block. The block and bullet rise together through a vertical distance of 8.6cm, as shown in figure below

(a) Calculate the change in gravitational potential energy of the block and bullet.

(b) Determine the initial speed of the block and the bullet, after they began to move off together

(c)Using the information in (b) and the principle of conservation of momentum, determine the speed of the bullet before the impact with the block.