1- A cylindrical hoop with a diameter of 58 cm has the same mass as a spherical
ID: 1784908 • Letter: 1
Question
1- A cylindrical hoop with a diameter of 58 cm has the same mass as a spherical shell of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere's radius in cm?
2- A 3 kg block and a 5 kg block are attached to opposite ends of a light rope. The rope hangs over a solid, frictionless pulley that is 22 cm in diameter and has a mass of 1.5 kg. When the blocks are released, what is the acceleration (magnitude) of the lighter block?
3- A 480 g, 26-cm-diameter plastic solid sphere is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 2500 rpm in 6.0 s?
Explanation / Answer
2)
F = ma = T- mg ...........(1)
F = ma = mg - T ............(2)
= rF = I = r(T- T)
Ia / r = r(T- T)
Ia / r² = (T- T) .............(3)
Adding (1), (2), and (3) together and solving for a
a = [g(m- m)] / ( m + m + I/r²)
a = [g(m- m)] / ( m + m + 0.5Mr²/r²)
a = [g(m- m)] / ( m + m + 0.5M)
a = [9.81m/s²(5 kg - 3 kg)] / [3 kg + 5 kg + 0.5(1.50 kg)]
a = 2.24 m/s²
3)
m = 0.480 kg
R = d/2 = 0.13 m
W = 2500*2/60 = 261.8 rad/sec
I = 1/2mR^2
I = 0.004056 kgm²
= w/t = w/6 = 43.63 rad/sec²
Torque = I* = 0.177 Nm
Not sure about first problem.
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