Biomedical measurements show that the arms and hands together typically make up
ID: 1411493 • Letter: B
Question
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 77.0 kg person having arms 70.0 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 12s. Assume that the arms and legs are kept straight.
A)What is the average angular velocity of his arms and legs?
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.
C)What is the total kinetic energy due to both his forward motion and his rotation?
D)What percentage of his kinetic energy is due to the rotation of his legs and arms?
Explanation / Answer
(A)mass of person=77 kg
mass of arm and hand=0.13*77=10.01 kg
mass of feet and legs=0.37*77=28.49 kg
angle covered in 12 sec =2*60 degree=2.094 rad/sec
average angular speed=1.047/12=0.1745 rad/sec
(B)moment of inertia of arm =10.01*0.7^2/3=1.635 kgm^2
moment of inertai of legs=28.49*0.92^2/3=8.038 kgm^2
rotational energy of arm=0.5*1.635*0.1745^2=0.0249 J
rottaional energy of legs=0.5*8.038*0.1745^2=0.1223 J
(C)velocity=12 km/hr=10/3 m/s
translatona kinetic energy=0.5*77*(10/3)^2=427.778J
total kinetic energy=427.925 J
(D) percent =0.034 percent
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