Question

M OR Copy chood T Do not assist al mg If the mass of the falling mass is 35.7 kg, the mass of the solid sphere is 17.2 kg and the radius is 0.30, calculatd the acceleration afin m/s2) in the string. (Hint: use the correct equations you selected in the previous problem. If you didn't keep the equations, you should rewrite the equations). Round off to TWO decimal places. Acceleration a =

Answer 1

The torque on the solid sphere, $\tau$ = R * T = I * $\alpha$
Where R is the radius of the sphere, T is the tension in the string, I is the moment of inertia of the sphere and $\alpha$ is the angular acceleration
The moment of inertia of a solid sphere, I = 2/5 * M * R²
$\alpha$ = a / R, where a is the acceleration of the system

Substituting these values,
R * T = 2/5 * M * R² * (a / R)
T = 2/5 * M * a ...(1)
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Consider the falling body.
m * g - T = m * a
Where m is the mass of the falling body.
Substituting (1),
m * g - 2/5 * M * a = m * a
m * g = a * [m + 2/5 * M]
a = (m * g) / [m + 2/5 * M] ...(2)
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Substituting values in (2),
a = (35.7 * 9.81) / [35.7 + 2/5 * 17.2]
= 8.22 m/s²