Question Part
Submissions Used
A 11.5-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.9 m/s, determine the following.
(a) the translational kinetic energy of its center of gravity
J
(b) the rotational kinetic energy about its center of gravity
J
(c) its total kinetic energy
J
a) 1/2 mv^2
b) 1/2 I (v^2/r^2)
Have to look up I for a cylinder
c) a + b
To determine the translational kinetic energy of the cylinder's center of gravity, you can use the formula:
Translational Kinetic Energy = (1/2) * mass * velocity^2
In this case, the mass of the cylinder is given as 11.5 kg and the speed of its center of gravity is given as 10.9 m/s. Plugging these values into the formula:
Translational Kinetic Energy = (1/2) * 11.5 kg * (10.9 m/s)^2
Calculating this expression will give you the answer in Joules (J).
To determine the rotational kinetic energy about its center of gravity, you can use the formula:
Rotational Kinetic Energy = (1/2) * moment of inertia * angular velocity^2
Since the cylinder rolls without slipping, it'll be treated as a solid disk, and the moment of inertia of a solid disk is given by the formula:
Moment of Inertia = (1/2) * mass * radius^2
In this case, the mass of the cylinder is again 11.5 kg, and to find the radius, we need more information such as the dimensions of the cylinder.
Once you have the radius, you can calculate the moment of inertia. The angular velocity is related to the linear velocity by the formula:
Angular Velocity = Velocity / Radius
Using this information, you can calculate the rotational kinetic energy.
To find the total kinetic energy of the cylinder, simply add the translational and rotational kinetic energies together.