# Work Done on the system

1. Mar 6, 2016

### Brandon 456

1. The problem statement, all variables and given/known data
An amusement park ride consists of a slide that is sloped an an angle of 30.9 degrees with respect to the vertical with a spring located at the top of the ramp with a spring constant of 186 N/m. A person will sit in a sled on the ramp, and then the spring is compressed by the operator an amount of 2.2 m. The spring is then released by the operator and person plus sled are pushed down the ramp by the spring. The sled will become separated from the spring once the spring returns to its rest length. Also, there is friction between the sled and the ramp which has a coefficient of kinetic friction of 0.7. Consider the person and sled as one object with a total mass of 55.7 kg.

After the person has traveled down the ramp a distance 5.5 m, the person will have a speed of 8.364 m/s, the spring has returned to its rest length and you determine that 648 J of thermal energy went into the ramp as the person travels this distance.

2. Relevant equations
Total work= DeltaKtranslational+ DeltaKRotational+ Ugravitational+ Uspring+ DeltaThermal + other

W=Fd
Work done by spring= (1/2)kx^2

3. The attempt at a solution

There were 11 total parts to this problem, first half of them invovled using EVERYTHING as the system, but the second half involved only using the person+sled as the system. I have solved all the problems except the work done on the system of the person+sled. I have the change in thermal, the work done by friction, change in kinetc and work done by gravity and by the spring. I would assume the work done on the system would be just adding up all the work done on it by various forces, but that was wrong. So would the work done on the system just be the everything excluding thermal/friction?

Thanks

2. Mar 6, 2016

### haruspex

You need to distinguish "work done by" from "work done on".
Work done by forces includes work that ends up as thermal energy or potential energy. Neither of these are considered work possessed by the person+sled system. (The gravitational potential energy is a property of the person+sled+earth system.)

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