Question

A force that varies with time is applied to an object. The force increases linearly from zero to twenty-four newtons during the first two seconds. Then, the force remains constant for four seconds. During the last two seconds, the force linearly decreases to zero newtons. What is the total impulse exerted on the object?

Answer 1

144Ns

Step-by-step explanation:

Impulse is the product of force and change in time or a measure of the change in momentum. Mathematically, Impulse is given as

J = FΔt

Where

J = Impulse,

F = Force,

Δt = change in time.

Due to the varying force, we know that the impulse varies at different points in the motion. Hence, the Net Impulse will be the addition of the individual impulses, i.e.

J = ΣJᵢ

J = J₁ + J₂ + J₃

J = F₁Δt₁ + F₂Δt₂ + F₃Δt₃

=> J = (24*2) + (24*4) + (0*2)

J = 48 + 96 + 0

J = 144 Ns