Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 9 - Center of Mass and Linear Momentum - Problems - Page 249: 32a

Answer

$p = (30.0~N\cdot s)~\hat{i}$

Work Step by Step

To find the impulse on the car, we can calculate the area under the force versus time graph. From $t = 0$ to $t = 4.0~s$, the area can be divided into two parts, including a triangle (0 to 2 s) and a rectangle (2 s to 4 s) We can find each area separately: $A_1 = \frac{1}{2}(10.0~N)(2.0~s) = 10.0~N\cdot s$ $A_2 = (10.0~N)(2.0~s) = 20.0~N\cdot s$ We can find the impulse from $t = 0$ to $t = 4.0~s$: $J = 10.0~N\cdot s +20.0~N\cdot s = 30.0~N\cdot s$ The change in the car's momentum will be equal to the impulse. Since the car started at rest, $p = 30.0~N\cdot s$ We an express the momentum in unit-vector notation: $p = (30.0~N\cdot s)~\hat{i}$
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