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Tarzan, whose mass is 94 kg, is hanging at rest from a tree limb. Then he lets go and falls to the ground. Just before he lets go, his cente
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Tarzan, whose mass is 94 kg, is hanging at rest from a tree limb. Then he lets go and falls to the ground. Just before he lets go, his center of mass is at a height 2.8 m above the ground and the bottom of his dangling feet are at a height 2.0 above the ground. When he first hits the ground he has dropped a distance 2.0, so his center of mass is (2.8 – 2.0) above the ground. Then his knees bend and he ends up at rest in a crouched position with his center of mass a height 0.5 above the ground.(a) Consider the point particle system. What is the speed v at the instant just before Tarzan’s feet touch the ground? v = _______ m/s. (b) Consider the extended system. What is the net change in internal energy for Tarzan from just before his feet touch the ground to when he is in the crouched position?
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Physics
4 years
2021-08-02T07:34:03+00:00
2021-08-02T07:34:03+00:00 1 Answers
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Answers ( )
Answer:
(a) 6.26 m/s
(b) -2,118.76 J
Explanation:
Here we have
Tarzan’s mass, m = 94 kg
Height of feet above ground, h₁ = 2.0 m
Height of center of mass above ground = 2.8 m
Height of center of mass on the ground, h₂ = 2.8 – 2.0 = 0.8 m
Height of center of mass in the crouched position, h₃ = 0.5 m
(a) The speed at the instant just before Tarzan’s feet touches the ground is given by;
v² = u² + 2·g·h₁
v = Speed at the instant just before Tarzan’s feet touches the ground
u = Initial speed = 0 m/s while hanging from the tree
g = Acceleration due to gravity
Therefore, v² = 2·g·h₁ = 2 × 9.8 × 2 = 39.2 m²/s²
∴ v = √(39.2 m²/s²) = 6.26 m/s
(b) Here we have
Just before Tarzan’s feet touches the ground internal energy is given by;
Initial Internal energy = K.E. + P.E. = m·g·h₂+ 0.5·m·v²
= 94 × 9.8 × 0.8 + 0.5 × 94 × 39.2 = 2,579.36 J
When in the crouched position, the final internal energy is given by;
m·g·h₃ = 94 × 9.8 × 0.5 = 460.6 J
Therefore net change in internal energy, ΔU is given by
ΔU = Final internal energy – Initial internal energy
ΔU = 460.6 J – 2,579.36 J = -2,118.76 J.