A block is placed on a frictionless ramp at a height of 14.5 m above the ground.

Question

A block is placed on a frictionless ramp at a height of 14.5 m above the ground. Starting from rest, the block slides down the ramp. At the bottom of the ramp, the block slides onto a frictionless horizontal track without slowing down. At the end of the horizontal track, the block slides smoothly onto a second frictionless ramp. How far along the second ramp does the block travel before coming to a momentary stop, as measured along the incline of the ramp? (Picture Included)

After the block comes to a complete stop on the second ramp, it will then begin moving back down the second ramp. What is the speed of the block when it is 8.25 m, vertically, above the ground?

A block is placed on a frictionless ramp at a height of 14.5 m above the ground Starting from rest, the block slides down the ramp. At the bottom of the ramp, the block slides onto a frictionless horizontal track without slowing down. At the end of the horizontal track, the block slides smoothly onto a second frictionless ramp. How far along the second ramp does the block travel before coming to a momentary stop, as measured along the incline of the ramp? After the block comes to a complete stop on the second ramp, it will then begin moving back down the second ramp. What is the speed of the block when it is 8.25 m, vertically, above the ground?

Explanation / Answer

applying conservation of enrgy we get

Ui=Uf

so mgh1= mgh2

so h1=h2

so h2= 14.5 m

thus distance moved along the ramp= 14.5/sin18.5

=45.697 m

2). Wgravity= Kf-Ki

= mg(14.5-8.25)=1/2*m*v^2

so V=sqrt(2*9.8*6.25)

= 11.06 m/s

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