Concept explainers
A small block of mass m = 200 g is released from rest at point Ⓐ along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P7.45). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point Ⓐ relative to point Ⓑ. (b) the kinetic energy of the block at point Ⓑ, (c) its speed at point Ⓑ, and (d) its kinetic energy and the potential energy when the block is at point Ⓒ.
Figure P7.45 Problems 45 and 46.
(a)
Gravitational potential energy.
Answer to Problem 45P
The gravitational potential energy is
Explanation of Solution
Write down the equation for gravitational potential energy
Here
Conclusion:
Substitute
The gravitational potential energy is
(b)
Kinetic energy of the block.
Answer to Problem 45P
The kinetic energy is
Explanation of Solution
Write the law of conservation of energy.
Here
At point A, kinetic energy is zero.
At point B, potential energy is zero.
Therefore,
Substitute (I) in (III)
Conclusion:
Substitute
The gravitational potential energy is
(c)
Velocity at point B.
Answer to Problem 45P
Velocity is
Explanation of Solution
Write down the equation for kinetic energy.
Here
Rewrite (V) in terms of
Conclusion:
Substitute
Velocity is
(d)
Kinetic energy and potential energy at point C.
Answer to Problem 45P
Potential energy is
Kinetic energy is
Explanation of Solution
Write down the equation for gravitational potential energy
Here
Write the law of conservation of energy.
Here
Rewrite (VIII)
At point A, kinetic energy is zero.
Therefore,
Conclusion:
Substitute
Substitute
Potential energy is
Kinetic energy is
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Chapter 7 Solutions
Principles of Physics: A Calculus-Based Text
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