Esther's 2 kg skateboard rolls at 3 m/s. She gives it one strong boost, and it rolls away at 7 m/s in the same direction.
By how much did the skateboard's momentum change?
Momentum change compares two moments: before and after.
Both momenta carry signs along one line, so name the positive direction first.
Take the skateboard's direction of travel as positive.
Before the boost: p_initial = 2 × 3 = 6 kg·m/s.
After the boost: p_final = 2 × 7 = 14 kg·m/s.
The change is final minus initial: Δp = p_final − p_initial.
Δp = 14 − 6 = 8 kg·m/s.
The boost added 8 kg·m/s of momentum.
A 3 kg cart speeds up from 2 m/s to 6 m/s. Take its direction of travel as positive. Enter its momentum change in kg·m/s.
A velocity that points the negative way takes a negative sign, and so does its momentum.
Always subtract in the same order: final minus initial.
A negative Δp means the object lost forward momentum, or swung over to the negative direction.
A 20 kg canoe glides at 4.5 m/s. Backpaddling slows it to 1.5 m/s, still in the same direction. Take its direction of travel as positive. Calculate its momentum change.
Write down the values:
m = 20 kg, v_initial = 4.5 m/s, v_final = 1.5 m/s, Δp = ?
Write down the equation:
Δp = p_final − p_initial
Substitute in the values, and calculate:
p_initial = 20 × 4.5 = 90
p_final = 20 × 1.5 = 30
Δp = 30 − 90 = −60
The canoe's momentum change is −60 kg·m/s: it lost 60 kg·m/s.
A 60 kg skater slows from 5 m/s to 1 m/s, still moving the same way. Take her direction of travel as positive. Enter her momentum change in kg·m/s (keep the sign).
A 0.5 kg ball hits a wall at 6 m/s and rebounds along the same line at 4 m/s. Take the direction toward the wall as positive. Calculate the ball's momentum change.
Write down the values:
m = 0.5 kg, v_initial = 6 m/s, v_final = −4 m/s (it rebounds), Δp = ?
Write down the equation:
Δp = p_final − p_initial
Substitute in the values, and calculate:
p_initial = 0.5 × 6 = 3
p_final is negative: p_final = 0.5 × (−4) = −2
Δp = −2 − 3 = −5
The ball's momentum change is −5 kg·m/s. The reversal makes the change bigger than a plain stop would be.
A 0.4 kg handball hits a wall at 8 m/s and rebounds along the same line at 3 m/s. Take the direction toward the wall as positive. Enter the ball's momentum change in kg·m/s (keep the sign).
A 4 kg scooter speeds up from 2.5 m/s to 6.5 m/s. Take its direction of travel as positive. Enter its momentum change in kg·m/s.
A 0.6 kg basketball hits a backboard at 8 m/s and rebounds along the same line at 5 m/s. Take the direction toward the backboard as positive. Enter the ball's momentum change in kg·m/s (keep the sign).
A 1 kg ball moves at 5 m/s. Case one: it hits soft clay and stops dead. Case two: it hits a springy net and bounces straight back at 5 m/s. Which statement about the size of the momentum change is correct?