C LEVEL PROBLEMS

1)What is the momentum of a 22-g sparrow flying with a speed of 8.1 m/s?

SOLUTION:

p = mv = (0.022 kg)(8.1 m/s) = 0.18 kg·m/s.

2)A tennis ball may leave the racket of a top player on the serve with a speed of 65.0 m/s. If the ball has a mass of 0.0600 kg and it is in contact with the racket for 0.300 s, what is the average force on the ball? Would this force be large enough to lift a 60-kg person?

SOLUTION:

We find the average force on the ball from

F = Dp/Dt = (Dmv/Dt) =[(0.0600 kg/s)(65.0 m/s) – 0]/(0.300 s) = 13 N.

Because the weight of a 60-kg person is » 600 N, this force is not large enough.

3)A 0.145-kg baseball pitched at 39.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between the bat and ball is 1.00 x 10-3 s, calculate the average force between the bat and the ball during contact.

SOLUTION:

We find the average force on the ball from

F = Dp/Dt = m Dv/Dt =(0.145 kg)[(52.0 m/s) – (– 39.0 m/s)]/(1.00 ´ 10–3 s) =1.32 ´ 104 N.

Your answer may or may not be off by a plus or minus sign depending on your choice of a coordinate syste.

4)The distance between a carbon atom (m = 12 u) and an oxygen atom (m = 16 u) in the CO molecule is 1.13 x 10-10 m. How far from the carbon atom is the center of mass of the molecule?

SOLUTION:

We choose the origin at the carbon atom. The center of mass will lie along the line joining the atoms:

xCM= (mCxC + mOxO)/(mC + mO) 

= [0 + (16 u)(1.13 ´ 10–10 m)]/(12 u + 16 u) =6.5 ´ 10–11 m from the carbon atom.

5)A 75 kg ice skater moving at 10 m/s crashes into a stationary skater of equal mass. After the collision, both skaters move as one with a speed of 5.0 m/s. The average force a human can endure without breaking a bone is 4500 N. If the impact time was 0.10 s, what was the force of impact on each skater and did a bone break?

SOLUTION:

Find the momentum of one of the skaters before and after the collision, then find the change in momentum. Recall that the change in momentum is just the impulse, or average force applied during some time interval. If you divide the impulse by the contact time, then we would get the average force experienced by each skater. Remember, due to action and reaction, the force experienced by each skater has equal magnitude but opposite directions. 

Pi = mvi = (75 kg)(10 m/s) = 750 kg-m/s

Pf = (m)vf = (75 kg)(5 m/s) = 375 kg m/s

DP = 375 – 750 = -375 kg m/s

F = DP/DT = (-375 kg m/s)/(0.10 s) = 3750 N

This force is less than 4500 N therefore no bones were broken.