Unit: Work and Energy Year: 1997 Question#: 21
Question: A cart of mass M on a frictionless track starts from rest at the top of a hill having height h1, as shown in the diagram below. What is the kinetic energy of the cart when it reaches the top of the next hill, having height h2?
(1 ) mgh1
(2 ) mg(h1-h2)
(3 ) mg(h2-h3)
(4 ) 0
What is this question really asking?
Explanation by: Rachel M
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Answer 1
mgh1
INCORRECT
This is the GPE (gravitational potential energy) of the cart at the top of the first hill. At the top of the second hill, the cart has GPE and KE. These two together must equal the GPE of the first hill in order to conserve energy. return to top
Answer 2
mg(h1-h2)
CORRECT
In order to conserve energy, the total energy at the top of both hill 1 and hill 2 must be the same. Therefore, GPE + KE (at h1) = GPE + KE (at h2)
The KE at h1 = 0 because the cart isn't moving yet. GPE = mgh, so at h1 the total energy = mgh1 + 0 = mgh1.
At h2, there is still GPE because there is a point lower than this one, this GPE= mgh2 and there is also some unknown KE since the cart is moving at this point. So at h2, total energy= mgh2 + KE. If energy is conserved, than the total energy from h1 can be transfered to this problem in place of the total energy. This creates mgh1= mgh2 + KE. Rearranging this equation creates KE = mgh1- mgh2. This can be simplified into
KE= mg (h1-h2).
return to top Answer 3
mg(h2-h3)
INCORRECT
You might have gotten this answer if you thought that mgh2= mgh3 + KE. This can not be true because there is KE at h2 ( that's what you're finding) and it is not the same as the KE at h3 because the mgh is different at each height. This could possibly be the answer if h2 was the highest point in the problem, but it's not. Also, the equation mentioned above would get you the KE for h3, not h2. return to top
Answer 4
0
INCORRECT
There has to be some KE at h2 because the cart is still moving. return to top
What's this question really asking?
Do you know that energy is conserved? Can you use this information and also the knowledge of the GPE at h1 and h2 to find the KE at h2? return to top
