A 55 kg boy takes a running start of 25 m/s at a 20 kg tire swing, jumping at it

Question

A 55 kg boy takes a running start of 25 m/s at a 20 kg tire swing, jumping at it horizontally and landing in a seated position. Before this happens, the tire was at a vertical distance of 0.25 m from the ground hanging vertically at rest from branch by a J.0 m rope. Consider a physical system of the boy, the tire, and the Earth a. Energy is *not* conserve during the brief moment in time when the boy jumps in the tier Explain what you would have to do to treat the motion instead b. Find the boy and tire swing's velocity right after he jumps into it. (You may want a different approach than conservation of energy) c. The tire and boy swing upwards after the child jumps in until they stop for a moment at the peak height of the swing. Is energy now conserved? Explain. d. Find the maximum height off the ground reached by the child and tire swing.

Explanation / Answer

a)The energy is not conserved in the given example. Since the swing has got the potential energy and the boy has kinetic energy of motion. The moment boy jumps on the swing the energy of the system is only kinetic energy and the gravitational PE of the swing does not add into the energy of the system

b)from conservation of momentum

Pi = Pf

m1v1 + m2v2 = (m1 + m2)Vf

vf = m1v1/(m1 + m2)

vf = 55 x 2.5/(55 + 20) = 1.83 m/s

Hence, Vf = 1.83 m/s

c)Yes, now the energy is conserved. Because, at the heighest point the kinetic energy of the system becomes zero and all the energy gets converted to potential energy.

d)PE = KE

(m1 + m2) g h = 1/2 (m1 + m2) vf^2

h = 0.5 vf^2/g = 0.5 x 1.83^2/9.81 = 0.171 m

Hence, h = 0.171 m

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