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posted by  ace112 on 7/22/2008 9:18:23 PM  |  status: Live  

Physics roller coaster problem

Course Textbook Chapter Problem
General Physics N/A N/A N/A
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Here's the question:

The roller coaster is dragged up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, 4.
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posted by Cdutch88 on 7/22/2008 9:43:21 PM  |  status: Live
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ace112's comment:
"Thanks! :D"
Response Details:
Conservation of total energy stipulates that in a closed system (with no external forces), the total energy at two different points will still remain the same.

In this problem, since there is no friction, this must be a closed system. That means that the total energy = gravitational potential energy + kinetic energy is constant.

Since the roller coaster is at rest at point 1, we know that it has no kinetic energy and thus its grav. potential energy is equal to its total energy. Since grav. potential energy is calculated by PE = mgh, the total energy here is m*g*35, where m represents the mass of the roller coaster and g is the acceleration of gravity.

Point 2:
TE = PE + KE = 0 + KE
35mg = 1/2 mv2
v = √(70g) = √(70*9.81)

Point 3:
TE = PE + KE
35mg = 28mg + 1/2 mv2
v = √(14g) = √(14*9.81)

Point 4:
TE = PE + KE
35mg = 15mg + 1/2 mv2
v = √(40g) = √(40*9.81)

Hope that helps!
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