At t=0 a 2150kg rocketship in outer space fires the engine which exerts a force=

Question

At t=0 a 2150kg rocketship in outer space fires the engine which exerts a force=At2, and F(1.25s)=781.25N in the x direction. Find the impulse J during the interval t=2.00s and t=3.5s At t=0 a 2150kg rocketship in outer space fires the engine which exerts a force=At2, and F(1.25s)=781.25N in the x direction. Find the impulse J during the interval t=2.00s and t=3.5s At t=0 a 2150kg rocketship in outer space fires the engine which exerts a force=At2, and F(1.25s)=781.25N in the x direction. Find the impulse J during the interval t=2.00s and t=3.5s

Explanation / Answer

As given in question

F(1.25) = 781.25 N

At^2 = 781.25

In this t = 1.25 secs

so,

A = 500

The obvious complication here is that the force is not constant, but is changing with time. That is the clue that signifies that you are going to have to use calculus.

We are told that F = A t^2

Recall that impulse is defined as force * time

I = F * t = A t^2 * t = A t^3

To calculate the impulse over the time period from 2 to 3.5 seconds, of a varying force, we must integrate I with respect to time. So,

I = At^3 dt from t = 2 to t = 3.5

I = A [t^4/4] from t=2 to t=3.5

I = A [ (3.5)^4 / 4 - (2.0)^4 / 4] = 500 [37.52 - 4] = 500 * 33.52 = 16760 Ns

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