Concept explainers
A 1.00-kg glider on a horizontal air track is pulled by a string at an angle θ. The taut string runs over a pulley and is attached to a hanging object of mass 0.500 kg as shown in Figure P5.40. (a) Show that the speed vx of the glider and the speed vy of the hanging object are related by vx = uvy, where u = z(z2 − h02)−1/2. (b) The glider is released from rest. Show that at that instant the acceleration ax of the glider and the acceleration ay of the hanging object are related by ax = uay. (c) Find the tension in the string at the instant the glider is released for h0 = 80.0 cm and θ = 30.0°.
Figure P5.40
(a)
To show: The speed of the glider and the speed of the hanging object are related by
Answer to Problem 76AP
The speed of the glider and the speed of the hanging object are related by
Explanation of Solution
Given info: The mass of the glider is
The free body diagram of the given case is as shown below.
Figure (1)
Form the above figure (1).
From the Pythagorean Theorem,
Here,
Rearrange the above equation for
The speed of the glider is.
Substitute
The term
Here,
Substitute
Substitute
Conclusion:
Therefore, the speed of the glider and the speed of the hanging object are related by
(b)
To show: The acceleration of the glider and the speed of the hanging object are related by.
Answer to Problem 76AP
The acceleration of the glider and the speed of the hanging object are related by.
Explanation of Solution
Given info: The mass of the glider is
From equation (2), the relation of
The acceleration of the glider is,
Substitute
The initial velocity is zero.
Substitute
Here,
Conclusion:
Therefore, the acceleration of the glider and the speed of the hanging object are related by.
(c)
The tension of the string.
Answer to Problem 76AP
The tension of the string is
Explanation of Solution
Given info: The mass of the glider is
From the free body diagram in figure (1) the net direction in
From part (a) the value of
Substitute
Substitute
Thus, the value of
The net force in
Here,
Substitute
Rearrange the above equation for
The net force in the
Here,
Form part (b) substitute
From equation (3) substitute
Substitute
Conclusion:
Therefore, the tension in the string is
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Chapter 5 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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