Question

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

Answer 1

`2.4√(L)` where L is the length of the ramp

Step-by-step explanation:

Let L (m) be the length of the ramp, and g = 9.81 m/s2 be the gravitational acceleration acting downward. This g vector can be split into 2 components: parallel and perpendicular to the ramp.

The parallel component would have a magnitude of

`gsin\theta = 9.81 sin17^o = 2.87 m/s^2`

We can use the following equation of motion to find out the final velocity of the book after sliding L m:

`v^2 - v_0^2 = 2a\Delta s`

where v m/s is the final velocity,
`v_0` = 0m/s is the initial velocity when it starts from rest, a = 2.87 m/s2 is the acceleration, and
`\Delta s = L` is the distance traveled:

`v^2 - 0 = 2*2.87*L`

`v = √(5.74L) = 2.4√(L)`