Explanation Concepts: A block slides with constant velocity down an inclined plane that has a slope angle θ . The block is then projected up the same plane with an initial speed v 0 . The distance travelled up the plane before coming to rest is based on the kinematic equation of motion. Explanations: Given: Constant velocity, slope angle of θ , and initial speed of v 0. Equations: The free-body diagram for the first part of this problem (when the block is sliding downhill with zero acceleration) is shown below. F → N is the normal force applied on the block and mg is the force of gravity, which also has two components. It is assumed in this case that friction acts in the upward direction and no acceleration (direction is chosen upward) occurs in the first case. m g s i n θ - f = m a = 0 ( 1 ) F N - m g c o s θ = 0 ( 2 ) f = μ k F N (3) Calculations: From Eqs. (1), (2) and (3), we get: m g s i n θ - μ k m g c o s θ = 0 ⟹ μ k = t a n θ (4) In the second case, when the block moves uphill and friction acts downward, we will have two equations of motion along the x and y axes as: m g s i n θ + f = - m a x ( 5 ) F N - m g c o s θ = 0 ( 6 ) From Eqs

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Question

Chapter 6, Problem 91P

To determine

To find:

(a) The distance the block travels up the plane before coming to rest.

(b) After the block comes to rest, whether it slides down the plane again.

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Chapter 6, Problem 90P

Chapter 6, Problem 92P

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Chapter 6 Solutions

Fundamentals of Physics Extended

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(a) The distance the block travels up the plane before coming to rest. (b) After the block comes to rest, whether it slides down the plane again.

Solution Summary: The author explains how the block slides with constant velocity down an inclined plane with a slope angle of theta and the kinematic equation of motion.

To find: (a) The distance the block travels up the plane before coming to rest. (b) After the block comes to rest, whether it slides down the plane again.

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Chapter 6 Solutions

To find:

(a) The distance the block travels up the plane before coming to rest.

(b) After the block comes to rest, whether it slides down the plane again.