Fundamentals of Physics Extended (10th Edition)

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

Chapter 8 - Potential Energy and Conservation of Energy - Problems - Page 204: 31c

Answer

4.00 m

Work Step by Step

Looking at the incline as a right triangle, we see that the change in height the block undergoes is Δh = d sin θ, where d is the distance traveled along the incline. From Problem 31b, we know that $ΔU_{g}$ = 39.2 J. So to find d, we can plug in these values in the equation for $ΔU_{g}$ and solve for d: $ΔU_{g}= mgΔh$ $ΔU_{g} = mgdsinθ$ $d = \frac{ΔU_{g}}{mg sin θ}$ $d = \frac{39.2 J}{(2.00 kg)(9.8 m/s²) sin 30.0^{\circ}}$ $d$ = 4.00 m
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