Person is oscillating between the horizontal positions of 1.5 m to 4.5 m. If the
ID: 1555437 • Letter: P
Question
Person is oscillating between the horizontal positions of 1.5 m to 4.5 m. If the person has a mass of 60 kg, and U = 0 at
y = 0.
Describe changes in the KE and PE of the skateboarder-Earth system between the positions of 3 m and 8.5 m and then from 8.5 m to 15 m, if 10 J of external work were done on the skateboarder-Earth system? Has the PE of the skateboarder-Earth system increased or decreased when the skateboarder moves from 3 m to 8.5 m?How would the KE of the skateboarder at 15 m compare to her KE at 3 m? Explain.
y m 10 10 x (m)Explanation / Answer
The kinetic energy of an object is given by K = ½ mv2, where v is the speed of the object and m is the mass of the object. Thus, the skater’s energy is greatest at the lowest point of the track, where the skater is moving the fastest.
The gravitational potential energy of an object is given by U=mgy where y is the object’s height above the potential energy reference, which is currently y=0. Thus, the skater’s potential energy is greatest where the skater is highest above the reference line.
So, from position 3m to 8.5m, the PE of the skateboarder- earth system will increase & its KE will decrease. Then, from 8.5m to 15m, the KE of the skateboarder- earth system will increase and its PE will decrease.
The law of conservation of energy states that the total energy in a system is constant. At any point along the track, the skateboarder has varying values for PE and KE, but at all points along the ramp the sum of PE and KE is constant.
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