A force acting on a particle increases uniformly from 0 to 20 N during the interval t = 0 to 1 s. It then decreases uniformly from 20 N at t = 1 s to −20 N at t = 3 s. If the net impulse from t = 0 to 3 s is N N·s, find N.
Physics · Center of maas , Momentum and Collision · impuse and question based on it
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Question

A force acting on a particle increases uniformly from 0 to 20 N during the interval t = 0 to 1 s. It then decreases uniformly from 20 N at t = 1 s to −20 N at t = 3 s. If the net impulse from t = 0 to 3 s is N N·s, find N.

Physics · Center of maas , Momentum and Collision · impuse and question based on it

G1 Physics · Accepted Answer

Impulse equals the signed area under the force-time graph. From 0 to 1 s, the graph is a triangle of base 1 s and height 20 N, so J₁ = (1/2)(1)(20) = 10 N·s. From 1 to 3 s, the force falls linearly from +20 N to −20 N, crossing zero at t = 2 s. The positive triangular area from 1 to 2 s is +10 N·s and the negative triangular area from 2 to 3 s is −10 N·s, so they cancel. Hence net impulse = 10 N·s and N = 10.