Solution: Because the impulse equals the change in momentum, you can reword this example to read, "What was the ball’s change in momentum?" It is also understood that the ball was initially at rest, so its initial speed was 0 m/s.
Given: m = 0.050 kg Unknown: Δp = ?
Δv = 75 m/s
Original equation: Δp = m*Δv
Solve: Δp = (0.050 kg)(75 m/s) = 3.75 kg m/s
Given: m = 0.12 kg; Unknown: F = ?
Δv = 20.0 m/s
Δt = 0.010 s
Original equation: F*Δt = m*Δv
Solve for the unknown: F = (m*Δv)/Δt
= (0.12 kg)(20.0 m/s)/(0.010 s)
= 240 N
The change in velocity of the ball is 46.0 m/s since the ball reversed direction. Thus, the change in momentum is (mass) x (change in velocity) = (0.060 kg)(46.0 m/s) = 2.8 kg m/s.
Use F = m*Δv/Δt => F = (0.060 kg)(46.0 m/s)/(0.020 s) => F = 140 N
3. If 300 million (300 000 000) people in the United States jumped up in the air simultaneously, pushing off the earth with an average force of 1000 N each for a time of 0.10 s, what would happen to the earth (mass = 6 000 000 000 000 000 000 000 000 kg)?
4. Bernie, whose mass is 70.0 kg, leaves a ski jump with a velocity of 21.0 m/s. What is Bernie’s momentum as he leaves the ski jump?
5. Ethel is sitting on a park bench feeding the pigeons when a child’s ball rolls toward her across the grass. Ethel returns the ball to the child by hitting it with her 2.0-kg purse with a speed of 20 m/s. If the impact lasts for 0.4 s, with what force does Ethel hit the ball?
6. When Sammy Sosa stepped up to the plate and hit a 0.150-kg fast ball traveling at 35.0 m/s, the impact caused the ball to leave his bat with a velocity of 45.0 m/s in the opposite direction. If the impact lasted for 0.002 s, what force did Sosa exert on the baseball?
1. (a) 5 400 000 000 kg m/s(b) The ship was so big that even if the iceberg had been spotted a kilometer away, the ship could not have been turned in time to avoid the iceberg.
2. -500 000 N
3. 0.000 000 000 000 5 m/s – this change in velocity is too small to be noticed!
4. 1470 kg m/s
5. 100 N
6. 6000 N