Question

A solid cylinder of mass 0.600 Kg rolls without slipping along a horizontal surface with a linear velocity of 5.0 m/s . It reaches an incline that makes an angle of 30° with the horizontal.

a- Ignoring the losses due to the friction, to what distance does the cylinder rise on the incline?

b- After reaching its maximum position on the incline, what will be its velocity at the bottom of the incline on its way back ?

Answer 1

This problem is basically the same as the one you posted earlier with the hollow sphere.
Use conservation of energy, as we did then.

Answer 2

you would need to know the radius of the cylinder to answer this. put simply, calc the linear *plus* rotational kinetic energy of the thing at the bottom of the slope, and that is how much gravitational potential energy it will have when it stops on the 30deg slope.

if it is all truly lossless, then when it returns to the bottom, the energy should have fully re-converted to KE (linear and rotational in the same amounts).

Answer 3

I calculated the height
Should I use the theta ? And how can I calculate the velocity at the bottom ?

Answer 4

Now you just need to convert this height to the distance travelled on the incline using sine 30°.

Velocity at the bottom is also related to conservation of energy.

Answer 5

D = 1.91 / sin 30 = 3.81 m
Now I will try to calculate the velocity

Answer 6

Correct, but... look at the value you have found.
Are you sure you had to solve an equation to answer that question?

Answer 7

no
so can I write v (bottom) = 5m/s ?
but why he is asking about it ugh ! " only those people who teach physics care "

Answer 8

Yes because at the bottom, you go back to the same height, so the KE must be the same as on the way up, so the speed is the same as-well. (the velocities are opposite).

Answer 9

Do you mean that v =-5 ?

Answer 10

v = 5 m/s ; \(\vec v = -5 \;\hat x\)