An amusement park ride consists of a slide that is sloped an an angle of 30.9 de

Question

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.

If you use the person plus sled as your system, what is the change in kinetic energy of the system?

= 1.948×103 J

If you use the person plus sled as your system, what is the change in thermal energy of the system?

4.323×102 J

If you use person plus sled as your system, what is the total work done on the system?
= ?????

If you use the person plus sled as your system, what is the work done by gravity on the system?
2.579×103 J

If you use the person plus sled as your system, what is the work done by the spring on the system?
4.501×102 J

If you use the person plus sled as your system, what is the work done by friction on the system?
-6.482×102 J

To get total work done, do I just add up all the work done, except friction because it is included in change in thermal, and just put a negative sign?

Explanation / Answer

To get total work done on the system = Work done by spring + Work done by gravity - work done by friction = Work done by gravity - heat generated
450.1 + 2579 - 648 = 2381J

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