The wheel weighs 70 kg, and is 120 cm in diameter. you mount the wheel by its ce

Question

The wheel weighs 70 kg, and is 120 cm in diameter. you mount the wheel by its central axis, wrap a string around the outer rim of the wheel and hang a 20 kg sandbag from the string, then allow it to drop from rest. The bag drops 3.77 m in 1.6 s.

A) What is the angular velocity of the wheel at the end of the fall?

B) Use energy methods to calculate the moment of inertia of the wheel.

C)Calculate the moment of inertia of the wheel as modelled by a hoop with radius of 60 cm.

D) Explain why your result in (B) was greater/less/ equal to you answer in (C)

Explanation / Answer

mg - T = ma ............................1

T x r = I x alpha.........................2

alpha = a /r................................3

T = I a / r^2..............................4

I = .5 x m x r^2 = .5 x 70 x .6^2 = 12.6 kgm^2

adding 1 and 4

mg = ma + 12.6/.6^2 a

20 x 9.8 = 20 a + 35a

55a = 196

a = 3.5636 m/s

alpha = 3.5636/.6 = 5.939 rad/s^2

3.77 m in 1.6 s

v^2 = u^2 + 2aS

v^2 = 2 x 3.5636 x 3.77

v bag = 5.18 m/s

for the wheel

w = alpha x t = 5.939 x 1.6 = 9.5024 rad/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.