a) A metal can containing condensed mushroom soup has a mass of 250g, a height o

Question

a) A metal can containing condensed mushroom soup has a mass of 250g, a height of 16.9cm, and a diameter of 6.31cm. It is placed at rest on its side at the top of a 2.99m long incline that is at an angle of 25.6° to the horizontal and is then released to roll straight down. Assuming energy conservation, calculate the moment of inertia of the can if it takes 1.72s to reach the bottom of the incline.

b) Enter the value of the quantity (if none enter 0) which is unnecessary for calculating the solution.

Explanation / Answer

It is placed at rest on its side, initial velocity = 0

s = ½ a t²

2.99 = ½ a 1.72²

a = 2.02 m/s²

torque T = f R = m g R cos

according to Newton's second law of rotational motion,

T = I = I (a/R) = m g R cos

= I a/(R²m g cos )

F = m a

m g sin - m g cos = m a

canceled all m, and remember that = I a/(R²m g cos )

g sin - I a/(R²m g cos ) g cos = a

g sin - I a/(R²m) = a

9.8 sin 25.6° - I (2.02)/(0.03155² * 0.250) = 2.02

I = 0.000272804 kg.m²

I = 2728.04 gr.cm²

b) Height = 16.9 is unnecessary

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