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A crate of mass M starts from rest at the top of a
Chapter 9, Problem 6E(choose chapter or problem)
A crate of mass M starts from rest at the top of a frictionless ramp inclined at an angle ? above the horizontal. Find its speed at the bottom of the ramp, a distance d from where it started. Do this in two ways: Take the level at which the potential energy is zero to be (a) at the bottom of the ramp with y positive upward, and (b) at the top of the ramp with y positive upward. (c) Why didn’t the normal force enter into your solution?
Questions & Answers
QUESTION:
A crate of mass M starts from rest at the top of a frictionless ramp inclined at an angle ? above the horizontal. Find its speed at the bottom of the ramp, a distance d from where it started. Do this in two ways: Take the level at which the potential energy is zero to be (a) at the bottom of the ramp with y positive upward, and (b) at the top of the ramp with y positive upward. (c) Why didn’t the normal force enter into your solution?
ANSWER:Solution 6E a) Mass of the crate is M. The angle is . The distance is d. Height of the ramp we can get by a little use of trigonometry. sin = height / d height = d sin . The potential energy at the top was “Mgh”. The potential energy at the bottom was zero. Kinetic energy at the top was zero and at the bottom was 1/2 MV . 2 By the conservation of mechanical energy, Mgh = 1/2 MV 2 g × d sin = 1/2 V 2 V = 2gd sin V = 2gd sin . T