Question

A cylinder of radius R = 8.00 cm is on a rough horizontal surface. The coefficient of kinetic friction between the cylinder and the surface is 0.250 and the rotational inertia for rotation about the axis is given by MR 2/2, where M is its mass. Initially it is not rotating but its center of mass has a speed of 9.0 m/s. After 3.00 s, what is the speed of its center of mass?

____________ m/s

Answer 1

The final speed of the cylinder's center of mass after 3 seconds is 13.1 m/s.

Step-by-step explanation:

To find the final speed of the cylinder's center of mass, we can use the principle of conservation of energy. The initial kinetic energy of the center of mass is given by 1/2 * M * (v^2), where M is the mass and v is the initial speed. The final kinetic energy is given by 1/2 * M * (vf^2), where vf is the final speed.

By setting the two equations equal to each other and solving for vf, we get vf =√(v^2 + 2 * g * h), where g is the acceleration due to gravity and h is the height the cylinder rolls down.

Plugging in the values, we get vf = √((9.0 m/s)^2 + 2 * 9.8 m/s^2 * 3.0 m) = 13.1 m/s.