Your best submission for each question part is used for your score. A single rol

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Your best submission for each question part is used for your score. A single roller-coaster car Is moving with speed v_0 on the first section of track when It descends a 5.0-m-decp valley, then climbs to the top of a hill that Is 4.1 m above the first section of track. Assume any effects of friction or of air resistance are negligible. What Is the minimum speed v_0 required If the car Is to travel beyond the top of the hill? m/s Can we affect this speed by changing the depth of the valley to make the coaster pick up more speed at the bottom? yes no Explain your answer. This answer has not boon graded yet. eBook interactive Example

Explanation / Answer

part a:

let zero potential energy referrence point be the first section of the track.

so initial potential energy=0

initial kinetic energy=0.5*mass*speed^2

height of the final point=4.1 m

final potential energy=mass*g*height=mass*g*4.1

for minimum v0, final speed at the final point=0 m/s

so final kinetic energy=0

conserving total mechanical energy:

initial potential energy+initial kinetic energy=final potential energy+final kinetic energy

==>0+0.5*mass*v0^2=mass*g*4.1+0

==>v0=sqrt(9.8*4.1/0.5)=8.9643 m/s

so the minimum speed is 8.9643 m/s

part b:

as the depth of the valley does not figure in the work-energy principle

,the speed can not be affected by changing the depth of the valley.

so answer is : NO.

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