Question

What would be the speed of a cart at the bottom of a very long frictionless inclined plane if it was released from rest at a height of 10.0 m above the bottom of the track? Assume the bottom of the track has height = 0. Show your work.

Answer 1

Step-by-step explanation:

Given

Height from which cart is released is
`h=10\ m`

as we know energy is Conserved and changes only its form so Potential Energy of Cart converted to kinetic Energy at bottom

Energy at Top
`E_T=mgh`

where m=mass of cart

g=acceleration due to gravity

h=height of track w.r.t bottom

Energy at bottom
`E_B=(1)/(2)mv^2`

`E_T=E_B`

`mgh=(1)/(2)mv^2`

cancel out common terms

`v=√(2* g* h)`

`v=√(2* 9.8* 10)`

`v=14\ m/s`