Calculating the average resistive force exerted

[JudgeA]

1. Homework Statement
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 traveling 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

Homework Equations

v²=u²+2as
F=ma

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.

 

[CWatters]

What do you know about energy and work?

 

[JudgeA]

What do you know about energy and work?

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

 

[Vector1962]

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

 

[haruspex]

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

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

 

[JudgeA]

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

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

 

[haruspex]

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

Yes.

 

[CWatters]

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

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.