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A metal can containing condensed mushroom soup has mass 215 g, height 10.8 cm, and diameter 6.38 cm. It is placed at rest on its side at the top of a 3.00 m long incline that is at 25.0 degrees to the horizontal, and it is then released to roll straight down. Assuming mechanical energy conservation, calculate the moment of inertia of the can if it takes 1.50 s to reach the bottom of the incline. Which pieces of data, if any, are unnecessary for calculating the solution

Answer :

hamzaahmeds

Answer:

I = 1.093 x 10⁻⁴ kg.m²

Here, all the other data, namely, the height of the can, length of the inclined plane, angle of inclination, time to reach the bottom, are unnecessary.

Explanation:

The can which is filled with the soup can be modelled as a solid cylinder. The moment of inertia of this solid cylinder about its axis of rotation can be given by the following formula:

[tex]I = \frac{1}{2}mr^2[/tex]

where,

I = moment of inertia of can = ?

m = mass of can with soup = 215 g = 0.215 kg

r = radius of can = diameter/2 = 6.38 cm/2 = 3.19 cm = 0.0319 m

Therefore,

[tex]I = \frac{1}{2}(0.215\ kg)(0.0319\ m)^2 \\[/tex]

I = 1.093 x 10⁻⁴ kg.m²

Here, all the other data, namely, the height of the can, length of the inclined plane, angle of inclination, time to reach the bottom, are unnecessary.

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