A solid cylinder rolls without slipping on a horizontal surface such that its center of mass moves at 5.0 m/s.If it has a total kinetic energy is 1.7 kJ,what is its mass?
A)140 kg
B)91 kg
C)68 kg
D)58 kg
E)45 kg

Question

Quizplus · Accepted Answer

The total kinetic energy of a rotating cylinder can be expressed as: 
KE = 1/2*I*w^2 + 1/2*m*v_cm^2, where I is the moment of inertia, w is the angular velocity, m is the mass, and v_cm is the velocity of the center of mass.

Since the cylinder is rolling without slipping, we know that: 
v_cm = w*R, where R is the radius of the cylinder.

We also know that: 
w = v_cm/R

Substituting this expression for w into the equation for KE, we can simplify it to:

KE = 1/2*m*v_cm^2*(1 + 1/2)

Simplifying this further, we have:

KE = 3/4*m*v_cm^2

Substituting the given values, we get:

1.7 kJ = 3/4*m*(5.0 m/s)^2

Solving for m, we get:

m = 91 kg

Therefore, the answer is B.

A Solid Cylinder Rolls Without Slipping on a Horizontal Surface