An amusement park ride consists of a slide that is sloped an an angle of 30.8 de

Question

An amusement park ride consists of a slide that is sloped an an angle of 30.8 degrees with respect to the vertical with a spring located at the top of the ramp with a spring constant of 216 N/m. A person will sit in a sled on the ramp, and then the spring is compressed by the operator an amount of 2.1 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 0.72. Consider the person and sled as one object with a total mass of 61.9 kg.

After the person has traveled down the ramp a distance 5.2 m, the person will have a speed of 8.088 m/s, the spring has returned to its rest length and you determine that 698 J of thermal energy went into the ramp as the person travels this distance

If you use everything as your system, what is the change in gravitational potential energy of the system?

Explanation / Answer

Spring is compressed by the amount d
Distance traveled down the ramp, l
change in hieght = lcos(theta)
change in PE = -mglcos(theta) = -61.9*9.8*5.2*cos(30.8) = -2.709 kJ

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