A physics textbook is placed on an inclined slope with an adjustable angle a. The coefficients of friction between the book and the slope are us = 0.5 and uk = 0.35 %3D respectively. 1m

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Chapter1: Units, Trigonometry. And Vectors
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A physics textbook is placed on an inclined slope with an adjustable angle a. The
coefficients of friction between the book and the slope are us = 0.5 and uk = 0.35
respectively.
1m
a
Transcribed Image Text:A physics textbook is placed on an inclined slope with an adjustable angle a. The coefficients of friction between the book and the slope are us = 0.5 and uk = 0.35 respectively. 1m a
(i) Initially the book is not moving. Copy the diagram and draw all the forces acting on
the book. Show mathematical expressions for the size (magnitude) of each force. If
we slowly increase the angle a, at what angle does the book start sliding?
(ii) Use the Work-Energy theorem to find a formula (expression) for the speed v of
the book when it reaches the bottom, in terms of the angle a.
(iii) If we place a ball of the same mass and material as that of book at the top, what
is the kinetic energy of the ball in terms of its mass and speed when it is rolling down
the ramp? Does friction (either static or kinetic) do any work on the rolling ball?
Explain your answer.
(Hint: the ball is a thin spherical shell)
(iv) We release the book and ball at the same time, and record which reaches the
bottom first. Which one wins? Is this true for all angles a?
(v) What happens to the objects as a becomes nearly 90°?
Transcribed Image Text:(i) Initially the book is not moving. Copy the diagram and draw all the forces acting on the book. Show mathematical expressions for the size (magnitude) of each force. If we slowly increase the angle a, at what angle does the book start sliding? (ii) Use the Work-Energy theorem to find a formula (expression) for the speed v of the book when it reaches the bottom, in terms of the angle a. (iii) If we place a ball of the same mass and material as that of book at the top, what is the kinetic energy of the ball in terms of its mass and speed when it is rolling down the ramp? Does friction (either static or kinetic) do any work on the rolling ball? Explain your answer. (Hint: the ball is a thin spherical shell) (iv) We release the book and ball at the same time, and record which reaches the bottom first. Which one wins? Is this true for all angles a? (v) What happens to the objects as a becomes nearly 90°?
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