Item A) A typical ten-pound car wheel has a moment of inertia of about 0.35kgm2.
ID: 1418682 • Letter: I
Question
Item A)
A typical ten-pound car wheel has a moment of inertia of about 0.35kgm2. The wheel rotates about the axle at a constant angular speed making 50.0 full revolutions in a time interval of 4.00s. What is the rotational kinetic energy K of the rotating wheel?
Item B)
The elastic energy stored in your tendons can contribute up to 35 % of your energy needs when running. Sports scientists have studied the change in length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters' tendons stretch 41 mm , while nonathletes' stretch only 33 mm . The spring constant for the tendon is the same for both groups, 33 N/mm . What is the difference in maximum stored energy between the sprinters and the nonathletes?
Item C)
How far must you stretch a spring with k = 1200 N/m to store 300 J of energy?
Explanation / Answer
(A)
I = 0.35 Kg m^2
w = 50.0/4 = 12.5 rev/s
w = 12.5 * (2*) rad/s
w = 78.5 rad/s
Rotational kinetic Energy of wheel is given by, K.Erotational = 1/2* I * w^2
K.Erotational = 1/2 * 0.35 * 78.5^2
K.Erotational = 1078.4 J
K = 1200 N/m
U = 300 J
We know,
Spring potential Energy is given by,
U = 1/2 * K * x^2
300 = 1/2 * 1200 * x^2
x = 0.707 m
Stretch in spring, x = 70.7 cm
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