(a)
Whether the sled will make it to the top of the second hump if no kinetic energy is given to the sled at the start of its motion.
(a)
Answer to Problem 5SP
Even if no kinetic energy is given to the sled at the start of its motion, the sled will make it up to the top of the second hump.
Explanation of Solution
Given info: The height of the first point is
Write the expression for the gravitational potential energy.
Here,
The value of
Substitute
Here,
Substitute
Here,
Find the difference in potential energy of the two points.
The difference in potential energy of the two points is
Conclusion:
Therefore even if no kinetic energy is given to the sled at the start of its motion, the sled will make it up to the top of the second hump.
(b)
The maximum height that the second hump could be in order for the sled to reach the top.
(b)
Answer to Problem 5SP
In order for the sled to reach the top of the second hump, the maximum height it can have is
Explanation of Solution
Given info: The work done against friction is
While moving, the potential energy of the system is converted to kinetic energy. The maximum height the second hump can have corresponds to the maximum kinetic energy gained during the motion. The maximum kinetic energy gained will be equal to the potential energy at the second hump.
Here,
Assume
Put equation (3) in (2) and solve for
Substitute
Conclusion:
Therefore in order for the sled to reach the top of the second hump, the maximum height it can have is
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