Question

A metal can containing condensed mushroom soup has mass 205 g, height 11.0 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 24.0° 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 · m2(b) Which pieces of data, if any, are unnecessary for calculating the solution? (Select all that apply.)the mass of the canthe height of the canthe angle of the inclinethe time the can takes to reach the bottomnone of these(c) Why can't the moment of inertia be calculated from

Answer 1

Answer: a) 0.000093 kg.m²

b) height of the can not required

Explanation:

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

s = ½ a t²

3 = ½ a 1.5²

a = 2.667 m/s²

torque T = f R = μ m g R cos Φ

according to Newton's second law of rotational motion,

T = I α = I (a/R) = μ m g R cos Φ

μ = I a/(R²m g cos Φ)

∑F = m a

m g sin Φ - μ m g cos Φ = m a

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

g sin Φ - I a/(R²m g cos Φ) g cos Φ = a

g sin Φ - I a/(R²m) = a

9.8 sin 24° - I (2.667)/(0.0319² * 0.205) = 2.667

3.86 - I x 2.667/0.000208 = 2.667

3.86 - 12822 x I = 2.667 m

I = 3.86 - 2.667 / 12822 = 1.193 / 12822 = 0.000093 kg.m²