A dock winch reels in a drifting boat. The boat needs a momentum change of 100 kg·m/s, and the winch line provides a steady 500 N net force.
How long must the winch run to deliver the 100 kg·m/s?
The second law in momentum form holds three quantities: F, Δp, and Δt.
This time the unknown has moved: you know F and Δp, and you want the time.
Start from F = Δp/Δt.
Make Δt the subject: Δt = Δp/F.
Substitute: Δt = 100/500 = 0.2 s.
A fifth of a second is enough.
A gentler force needs longer: the same Δp with a smaller F gives a bigger Δt.
A winch line provides a steady 500 N net force, and the boat needs a momentum change of 100 kg·m/s. Calculate the time the force must act.
Write down the values:
Δp = 100 kg·m/s, F = 500 N, Δt = ?
Write down the equation:
F = Δp/Δt
Make Δt the subject:
Δt = Δp/F
Substitute in the values, and calculate:
Δt = 100/500 = 0.2
The winch must run for 0.2 s.
A braking cart must lose 60 kg·m/s of momentum. The braking force averages 150 N. Calculate the time it must act (sizes only).
Write down the values:
Δp = 60 kg·m/s, F = 150 N, Δt = ?
Write down the equation:
Δt = Δp/F
Substitute in the values, and calculate:
Δt = 60/150 = 0.4
The braking force must act for 0.4 s.
A 120 N net force must change a paddleboat's momentum by 36 kg·m/s. Enter the time it must act in s.
A 25 N net force must change a wagon's momentum by 45 kg·m/s. Enter the time it must act in s.
A 600 N net force must change a rowboat's momentum by 150 kg·m/s. Enter the time it must act in s.
A 32 N net force must change a cart's momentum by 48 kg·m/s. Enter the time it must act in s.
Haruki paddles his canoe with strokes that average a 200 N net force. The canoe needs a momentum change of 90 kg·m/s. Enter the time the force must act in s.
An airport tug applies a steady 14000 N net force to a regional jet that needs a momentum change of 42000 kg·m/s. Enter the time the force must act in s.