Concept explainers
(a)
To find: The rank of the carts by kinetic energy before they meet the incline.
(a)
Answer to Problem 31A
The kinetic energy of the carts is ranked from highest to lowest is
Explanation of Solution
Given:
And,
Formula used:
The kinetic energy is
Where, m is the mass and v is the velocity of the cart.
Calculation:
Now calculate the kinetic energy of the given cart by using the given values such that
Conclusion:
Thus, the decreasing order of kinetic energy is
(b)
To Find: The rank of the carts by how high they go up.
(b)
Answer to Problem 31A
The rank of the height from highest to lowest is
Explanation of Solution
Given info.
And,
And, the calculated kinetic energies are 8J, 9J, 6J, and 2J.
Formula used:
The height can be calculated by the formula:
Here,
Calculation:
The height can be calculated by using the above formula for the respective cases,
Conclusion:
Thus, the decreasing rank is
(c)
To find: The rank of the carts by potential energy.
(c)
Answer to Problem 31A
The rank of the potential energy from highest to lowest is
Explanation of Solution
Given info.
And,
And, the calculated kinetic energy are 8J, 9J, 6J, and 2J.
Formula used:
The height can be calculated by the formula,
Here,
Calculation:
When the cart reaches the highest point on the incline, then the potential energy at the top is equal to the kinetic energy at the bottom. Therefore, the rank of the potential energy from the highest to lowest is
Conclusion:
Thus, the order is
(d)
To explain: The difference between the answers for b and c.
(d)
Answer to Problem 31A
Answers are different for b and c because the potential energy at the top is equal to the kinetic energy at the bottom.
Explanation of Solution
Given info.
And,
And, the calculated kinetic energy are 8J, 9J, 6J, and 2J.
The potential energy at the top is equal to the kinetic energy at the bottom, which is given as,
Conclusion:
Therefore, the answer is different for both options.
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