## A 76 kg bike racer climbs a 1500-m-long section of road that has a slope of 4.3 ∘ . you may want to review ( pages 296 – 298) . part a by ho

Question

A 76 kg bike racer climbs a 1500-m-long section of road that has a slope of 4.3 ∘ . you may want to review ( pages 296 – 298) . part a by how much does his gravitational potential energy change during this climb

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2022-06-27T23:44:37+00:00
2022-06-27T23:44:37+00:00 1 Answer
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## Answers ( 1 )

The change in potential energy of the bike racer is equal to

[tex]Delta U = mgDelta h[/tex]

where m is the mass of the bike racer, [tex]g=9.81 m/s^2[/tex] and [tex]Delta h[/tex] is the change in altitude of the racer. This [tex]Delta h[/tex] corresponds to the height of the ramp, which is [tex]L=1500 m[/tex] long. Therefore the height of the ramp (and the variation of altitude) is

[tex]Delta h=L sin (4.3^{circ})=112.5 m[/tex]

And so, the variation of potential energy of the racer is

[tex]Delta U = mgDelta h=(76 kg)(9.81 m/s^2)(112.5m)=8.39 cdot 10^4 J[/tex]