For a net force acts on a object according to the expression F_x(t)=F_0 ! ( t T )…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum

Problem

For

0\le t\le T

a net force acts on a

0.20\text{ kg}

object according to the expression

F_x(t)=F_0\sin\!\left(\frac{\pi t}{T}\right)

where

F_0=50\text{ N}

and

T=0.10\text{ s}

. For

t<0

and

t>T

, the net horizontal force is zero. The object is initially at rest. (a) Derive an expression, in terms of

F_0

and

T

, for the total impulse delivered to the object during the interval

0\le t\le T

. (b) Using the given numerical values, calculate the numerical value of the impulse. (c) Determine the object’s speed immediately after

t=T

. (d) Suppose instead that the net force follows

F_x(t)=F_0\sin\!\left(\tfrac{2\pi t}{T}\right)

for

0\le t\le \tfrac{T}{2}

and is zero afterward. Calculate the impulse in this modified case and state the percentage difference compared with the impulse found in part (b).