A crash test: the sled stops hard, and the belt holds the 70 kg dummy. The dummy slows from 15 m/s to 5 m/s in 0.2 s.
How hard does the belt hold the dummy back, on average, during the 0.2 s?
During the stop, the belt's force rises and falls from instant to instant.
F = Δp/Δt cannot follow every instant. It gives the average net force over the whole stop.
Take the dummy's direction of travel as positive.
Find the momentum change first, then divide by the time.
Momentum before: 70 × 15 = 1050 kg·m/s.
Momentum after: 70 × 5 = 350 kg·m/s.
Δp = 350 − 1050 = −700 kg·m/s.
F = Δp/Δt = −700/0.2 = −3500 N.
The minus sign says the net force points backward, against the dummy's motion.
Its size is 3500 N.
A belt slows a 70 kg crash-test dummy from 15 m/s to 5 m/s in 0.2 s. Take the dummy's direction of travel as positive. Calculate the average net force on the dummy.
Write down the values:
m = 70 kg, v_initial = 15 m/s, v_final = 5 m/s, Δt = 0.2 s, F = ?
Write down the equation:
F = Δp/Δt
Find the momentum change:
p_initial = 70 × 15 = 1050
p_final = 70 × 5 = 350
Δp = 350 − 1050 = −700
Substitute in the values, and calculate:
F = −700/0.2 = −3500
The average net force is −3500 N: 3500 N pointing backward, against the motion.
Haruki's 60 kg bumper car speeds up from 2 m/s to 5 m/s in 1.5 s. Calculate the average net force on it.
Write down the values:
m = 60 kg, v_initial = 2 m/s, v_final = 5 m/s, Δt = 1.5 s, F = ?
Write down the equation:
F = Δp/Δt
Find the momentum change:
p_initial = 60 × 2 = 120
p_final = 60 × 5 = 300
Δp = 300 − 120 = 180
Substitute in the values, and calculate:
F = 180/1.5 = 120
The average net force is 120 N, pointing forward.
A 40 kg cart speeds up from 3 m/s to 7 m/s in 2 s. Enter the average net force on it in N.
Take the truck's direction of travel as positive. An 800 kg truck slows from 12 m/s to 9 m/s in 2 s. Enter the average net force on it in N (keep the sign).
Take the direction toward the wall as positive. A 0.4 kg ball hits a wall at 6 m/s and rebounds along the same line at 3 m/s; the contact lasts 0.2 s. Enter the average net force on the ball in N (keep the sign).
A 75 kg sprinter accelerates from 3 m/s to 9 m/s in 3 s. Enter the average net force on the sprinter in N.
Take the car's direction of travel as positive. Wilma's 1100 kg car slows from 21 m/s to 15 m/s in 4 s of gentle braking. Enter the average net force on it in N (keep the sign).
An 8 kg wagon slows from 6 m/s to 1 m/s in 2 s. Which calculation gives the size of the average net force on it?