A metal can containing condensed mushroom soup has mass 220 g, height 10.0 cm an
ID: 1460239 • Letter: A
Question
A metal can containing condensed mushroom soup has mass 220 g, height 10.0 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 32.0° 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 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 = 0.5mr2 for the cylindrical can?
Explanation / Answer
(a)
net torque = I*alfa
r*m*g*sintheta = I*w/t
w = m*g*sintheta*r*t/I
initial potential energy = E1 = m*g*L*sintheta
final kinetic energy = E2 = 0.5*I*w^2
0.5*I*(m*g*sintheta*r*t/I)^2 = m*g*L*sintheta
0.5*r^2*t^2*m*g*sintheta/I = L
0.5*0.22*9.8*sin32*0.0369^2/I = 3
I = 0.00026 kg m^2
(b)
the height of the can
(c)
0.5*m*r^2 is used fr solid cylinder
the given cylinder is not solid