A fan cart glides along a track with its fan running steadily. Over 2 s, the cart's momentum climbs by 10 kg·m/s.
Its momentum climbed 10 kg·m/s in 2 s. What net force is the fan providing? You met Newton's second law earlier in the course as a = F_net/m; the same law answers this, written another way.
Newton's second law can be written in momentum language: the net force on an object equals the rate of change of its momentum.
net force = momentum change ÷ time taken
In symbols: F = Δp/Δt.
Δp/Δt is the rate of change of momentum: how much momentum changes each second.
This is not a new law. It is the same second law you mastered as a = F_net/m, re-expressed.
Why the two forms always agree is the next lesson's job.
The fan cart: Δp = 10 kg·m/s over Δt = 2 s, so F = 10/2 = 5 N.
A sail cart's momentum rises by 28 kg·m/s over 4 s. Enter the net force on it in N.
Which statement is what F = Δp/Δt says?
A falling momentum works too: when the momentum drops, Δp is negative, and the net force points the negative way.
A fan cart's momentum climbs by 10 kg·m/s over 2 s. Calculate the net force on it.
Write down the values:
Δp = 10 kg·m/s, Δt = 2 s, F = ?
Write down the equation:
F = Δp/Δt
Substitute in the values, and calculate:
F = 10/2 = 5
The fan provides a net force of 5 N.
Take a braking wagon's direction of travel as positive. Its momentum changes by −24 kg·m/s over 3 s. Calculate the net force on it.
Write down the values:
Δp = −24 kg·m/s, Δt = 3 s, F = ?
Write down the equation:
F = Δp/Δt
Substitute in the values, and calculate:
F = −24/3 = −8
The net force is −8 N: 8 N pointing backward, against the motion.
Gunnar says: 'F = Δp/Δt and the earlier a = F_net/m are the same law, written two ways.' Is Gunnar correct?
A rope's steady force raises a crate's momentum by 45 kg·m/s in 0.5 s. Enter the net force on the crate in N.
Four carts each change momentum as described. Which cart needs the largest net force?
Take the bus's direction of travel as positive. A braking bus's momentum changes by −600 kg·m/s over 4 s. Enter the net force on it in N (keep the sign).