an object moves with kinetic energy E on a horizontal plane then rises up a smooth with inclined plane. when the speed of the object on the inclined plane is half of that on the horizontal plane what is the potential energy of the object?
answer: 3/4E
hi
change Ec = change in Ep
vf = v/2 and vi = v
we note E = 1/2mvi²
1/2mvf² - 1/2mvi² = mgh - 0
1/2m(v/2)² - 1/2mv² = mgh
mv²/8 - 1/2mv² = mgh
-3/8mv² = mgh (i’m ignoring the negative sign since energy is scalar)
we note E = 1/2mvi²
so 3/8mv² = 3/4 * 1/2m² = 3/4 * E