A metal can containing condensed mushroom soup has mass 225 g, height 10.6 cm an

Question

A metal can containing condensed mushroom soup has mass 225 g, height 10.6 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 20.0 to the horizontal and is then released to roll straight down. It reaches the bottom of the incline after 1.50 s. (a) Assuming mechanical energy conservation, calculate the moment of inertia of the can. I = kg middot m^2 (b) which pieces of data, if any, are unnecessary for calculating the solution? (select al that apply.) the mass of the can the height of the can the angle of the incline the time the can takes to reach the bottom none of these (c) Why can't the moment of inertia be calculated from I = 1/2 mv^2 for the cylindrical can? Because since it is a cylinder its Mol requires the use of a different formula.

Explanation / Answer

here,

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

s = 0.5 a t^2

3 = 0.5 a 1.5^2

a = 2.667 m/s^2

torque T = f R = u m g R cos (phi)

according to Newton's second law of rotational motion,

T = I alpha = I (a/R) = u m g R cos (phi)

u = I a/(R^2m g cos (phi))

sigma F = m a

m g sin (phi) - u m g cos (phi) = m a

canceled all m, and remember that u = I a/(R^2m g cos (phi))

g sin (phi) - I a/(R^2m g cos (phi)) g cos (phi) = a

g sin (phi) - I a/(R^2m) = a

9.8 sin(20) - I * (2.667)/(0.0319^2 * 0.225) = 2.667

I = 5.88 * 10^-5 kg.m^2

b)

the height of the can is not required

c)

it can not be find out by simply I = 0.5 * m * r^2

as the soup is not uniform inside the metal can

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