Question

A 17kg box is on incline plane. the plane has no friction and the ramp is at an angle of 60 degrees. The vertical ramp height is 3.0 meters.

a. What will be the velocity of the box when it gets to the bottom of the ramp? (Use PE and KE to solve this)
b. How much work is done by gravity do make the box achieve the velocity in part a?
c. Keep in mind that friction is not part of this problem But if it were, how would things change?
d. If Friction were present, would you still be able to use the PE KE method to solve for the velocity at the bottom of the ramp? Explain.

Answer 1

a)
`v\approx 7.671\,(m)/(s)`, b)
`\Delta W_(g) = 500.157\,J`, c) Lower final velocity, d) No.

Step-by-step explanation:

a) The final velocity of the box is obtained by means of the Principle of Energy Conservation:

`K = U`

`(1)/(2)\cdot m \cdot v^(2) = m\cdot g \cdot \Delta h`

`v = √(2\cdot g \cdot \Delta h)`

`v = \sqrt{2\cdot \left(9.807\,(m)/(s^(2)) \right)\cdot (3\,m)}`

`v\approx 7.671\,(m)/(s)`

b) The work done by gravity is:

`\Delta W _(g) = m\cdot g \cdot \Delta h`

`\Delta W_(g) = (17\,kg)\cdot \left(9.807\,(m)/(s^(2)) \right)\cdot (3\,m)`

`\Delta W_(g) = 500.157\,J`

c) The presence means that final velocity will be lesser at the bottom.

d) No, since work losses need to be calculated in order to calculate final velocity