A Big Kid (53 kg) and a Little Kid (37 kg) take turns jumping upand down on a tr

Question

A Big Kid (53 kg) and a Little Kid (37 kg) take turns jumping upand down on a trampoline. The force exerted on each of thechildren by the trampoline is equivalent to a spring force with aconstant of 6000 N/m. At the highest point of the bounce,each child is 1 meter above the level surface of the trampoline. Inother words, they fall one meter from the highest point of theirmotion before contacting the trampoline.

1)      What maximum distance does thetrampoline depress for each kid?

(Hint: Use conservation ofenergy.)

2)      What is the period of oscillationfor each kid?

(Hint: The oscillationconsists of two parts: (1) the child is in contact with thetrampoline and (2) the child is in free-fall motion under theinfluence of gravity.)

Assume that the children are not pumping their legs, but aresimply bouncing passively on the trampoline.

You should assume that the motion of child when in contact withthe trampoline is exactly one half of a period of a simple harmonicoscillation. This is an approximation, since the equilibriumposition is not exactly at the point where they first touch thetrampoline.

Explanation / Answer

A Big Kid (53 kg) and a Little Kid (37 kg) take turns jumping upand down on a trampoline. The force exerted on each of thechildren by the trampoline is equivalent to a spring force with aconstant of 6000 N/m. At the highest point of the bounce,each child is 1 meter above the level surface of the trampoline. Inother words, they fall one meter from the highest point of theirmotion before contacting the trampoline.

1)      What maximum distance does thetrampoline depress for each kid?

(Hint: Use conservation ofenergy.)

1/2kx*x=53*9.8*1

0.5*6000*x*x=53*9.8

hence x=0.1731m for 53kg kid

for little kid

1/2kx*x=37*9.8*1

0.5*6000*x*x=37*9.8

hence x=0.1208m for 53kg kid

2)      What is the period of oscillationfor each kid?

T=2*3.1453/6000=0.5902sec for 53kg kid

T=2*3.1437/6000=0.4931sec for37kg kid

(Hint: The oscillationconsists of two parts: (1) the child is in contact with thetrampoline and (2) the child is in free-fall motion under theinfluence of gravity.)

Assume that the children are not pumping their legs, but aresimply bouncing passively on the trampoline.

You should assume that the motion of child when in contact withthe trampoline is exactly one half of a period of a simple harmonicoscillation. This is an approximation, since the equilibriumposition is not exactly at the point where they first touch thetrampoline.

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