# Calculating the average resistive force exerted

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1. Jan 28, 2017

### JudgeA

1. The problem statement, all variables and given/known data
In a theme park ride, a cage containing passengers falls freely a distance of 30 m from A to B and travels in a circular arc of radius 20 m from B to C. Assume that friction is negligible between A and C. Brakes are applied at C after which the cage with its passengers travels 60 m along an upward sloping ramp and comes to rest at D. The track, together with relevant distances, is shown in the diagram. CD makes an angle of 20° with thehorizontal.

(iv) Calculate the average resistive force exerted by the brakes between C and D.

From previous questions I know
Velocity at C = 31.3 m/s²
I know the cage and passengers travelling between C and D has a mass of 620kg
I know the cage gained 1.25*10⁵J of gravitational potential energy between C and D
2. Relevant equations
v²=u²+2as
F=ma

3. The attempt at a solution
I used v²=u²+2as to find an acceleration of 8 m/s² but didn't know how to proceed from there. If anyone could point me in the right direction that would be very helpful thanks.

2. Jan 28, 2017

### CWatters

What do you know about energy and work?

3. Jan 28, 2017

### JudgeA

I know the cage gained 1.25*10⁵J of gravitational potential energy between C and D (just added that to the main question)

4. Jan 28, 2017

### Vector1962

What is the total energy (PE+KE) at C and what is the total energy (PE+KE) at D?

5. Jan 28, 2017

### haruspex

What about the energy changes from start to finish of the ride?

6. Jan 29, 2017

### JudgeA

Kinda confused, so do I do 1/2mv² to find the kinetic and then mgh for potential?

7. Jan 29, 2017

### haruspex

Yes.

8. Jan 30, 2017

### CWatters

The ride starts with PE which is converted to KE on the way down to point C. Some of that KE is then converted back to PE on the way up the ramp to point D. The remainder of the KE has to be absorbed by the braking system.

So far you haven't mentioned how to calculate the work done by the braking system.