Solid Ramp
A ramp winds drive ..?
A solid aluminum disk rolls without slipping on a flat surface at a constant speed of 1.95 m / s. The disk rolls up the ramp 30 degrees to achieve maximum height. Compute h? Thank you very much for your time and help.
Unfortunately, response of other just below it overlooked that the drive has both linear and angular kinetic energy (as noted in Cat the following answer down). Thus, the total kinetic energy mv ^ TE = 1 / 2 2 + 1 / 2 Iw ^ 2 = KE, where I = 1 / 2 2 ^ mr is the inertia disk, r is the radius of the disc, m is its mass, and w is the angular velocity that rolls down the ramp. [See source.] At the bottom of the ramp, TE = KE = 2.1 (2 ^ mv + 1 / 2 mv ^ 2) = 4.3 mv ^ 2 where v = wr = 1.95 mps, which is the linear velocity and the tangential velocity along the rolling disk. As you can clearly see, the total kinetic energy is 50% higher than it would if the disk is not rotating (rolling). In all cases, top of the ramp up its role, all that kinetic energy has been converted into potential energy. Thus, PE = mgh = 3 / 4 KE = mv ^ 2 and the maximum height reached H = 3 / 4 v ^ 2 / g, where g = 9.81 m / sec ^ 2. You can do the math. The physics is this ... you can not ignore KE rotation. While the disc has two linear and angular KE, which must be taken into account. In addition, the angle of the ramp has no effect on the problem (Within reason). That is, whatever the angle, as long as the disc can roll up to it, the height H max = v ^ 3 / 4 2/g...period. What will change with the angle is how far along the ramp, the disk must travel to get to H = S sin (theta), where S is the distance along the ramp angle theta. With what you have, you can also find S.
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