
(a)
Speed of cart at point 3.
(a)

Answer to Problem 39P
The speed is
Explanation of Solution
Speed of cart at point 1 is
Potential energy is measured with respect to point 1.
Potential energy at the level of point 1 is taken as zero. Write the equation for total energy of at point 1.
Here,
Write the equation for total energy of at point 3.
Here,
According to the law of conservation of energy, the total energy at point 1 and 3 will remains the same. Equate the right hand sides equations (I) and (II).
Rewrite the above equation in terms of
Conclusion:
Substitute
Therefore, the speed is
(b)
Check whether the cart will reach the point 4 or not.
(b)

Answer to Problem 39P
Yes. The car will reach point 4.
Explanation of Solution
Speed of cart at point 1 is
Rewrite equation (III) by replacing
Here,
Write the condition for the cart to reach 4.
Conclusion:
Substitute
Since the condition satisfies, cart can reach at point 4.
Substitute
Therefore, the cart can reach at point 4.
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