Part C What is the total kinetic energy due to both his forward motion and his r

Question

Part C

What is the total kinetic energy due to both his forward motion and his rotation?

Biomedical measurements show that the arms and hands together typically make up 13.0 % of a person's mass, while the legs and feet together account for 37.0 % . For a rough (but reasonable) calculation, we can model the arms and legs as thin uniform bars pivoting about the shoulder and hip, respectively. Let us consider a 70.0 kg person having arms 68.0 cm long and legs 92.0 cm long. The person is running at 12.0 km/h , with his arms and legs each swinging through ±30 in 1/2s. Assume that the arms and legs are kept straight.

Part A What is the average angular velocity of his arms and legs?

Part B Using the average angular velocity from part A, calculate the amount of rotational kinetic energy in this person's arms and legs as he walks.

Part C What is the total kinetic energy due to both his forward motion and his rotation?

Part D What percentage of his kinetic energy is due to the rotation of his legs and arms?

Explanation / Answer

a)angular velocity=ang.displacement/time
=60degrees/1sec
=(pi/3)/1sec=1.04rad/sec.

b)rotational kinetic energy=0.5(moment of inertia)(ang.velocity)^2
for arms,MOI=ml^2/3(assumed as rod)where m=13%0f 70kg.length is given and ang. velocity as above.
for legs,MOI=ml^2/3(assumed as rod)where m=37%of 70kg.length is given and ang. velocity as above.
on solving,rotational kinetic energy=
0.5*(0.12*70*0.68^2/3)*(1.4)^2 = 1.37 for arms
and 7.16 for legs

So. KI = 8.53 J

c)kinetic energy due to his forward motion=0.5(70)(3.33)^2= 388.1115 joule.
total=388.1115+8.53= 396.64 joule.

d) percentage =kinetic energy due to rotation/total kinetic energy *(100)
=8.53/396.64*(100)=2.1%

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