A student of mass 50.0 kg swings on a playground swing, which is very light comp
ID: 1386557 • Letter: A
Question
A student of mass 50.0 kg swings on a playground swing, which is very light compared to the student. A friend releases the seat of the swing from rest at a height of 1.00 m above the lowest point of the motion. The student swings down and, at the lowest point of the motion, grabs a jug a water of mass 4.00 kg. The jug is initially at rest on a small table right next to the swing, so it does not move vertically as the student grabs it. The student keeps swinging foward while holding the jug; and the seat reaches amaximum height H1 above the lowest point. Air resistance and friction are negliable.
(A) Indicate whether H1 is greater than, less than, or eqaul to 1.00m. Justify your answer qualitatively, with no equations or calculations
(B) Explain how H1 can be calculated. You need not to do the calculations, but provide complete instructions so that another student could use them to calculate H1.
(C) The student now swings backward toward the starting point. At the lowest point of the motion, the student drops the water jug. Indicate whether the new maximum height the seat reaches is greater than, less than, or equal to H1. Justify your answer.
Explanation / Answer
1. It is less than, as it now has greater mass, but the total nergy is conserved. Thus, less height is needed to get the same potential energy. H1 < 1.00 m.
2.
The total mechanical energy at the beginning and at the end of the swing is conserved.
Note that the the left and right ends, both velocities are 0.
Please use these information in conservation of mechanical energy to get H1.
3.
The new maximum height is GREATER THAN H1, as the mass has decreased from the same amount of energy.Thus, greater height is needed to get the same amount of potential energy.
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