Abbie and Bonita decide to race up a hill that is 30 meters high. Abbie takes a

Question

Abbie and Bonita decide to race up a hill that is 30 meters high. Abbie takes a path that is 60 meters long while Bonita uses a path that is 100 meters long. It takes Abbie 60 seconds since her route is steep, while Bonita runs up her path in 30 second. They both start from rest at the sme hegith and stop at the top. Abbie has a weight of 700 N while Bonita has a weight of 500 N.

a) is the work that Abbie does in going up the hill great than, less than, or the same as the work that Bonita does in going up the hill?

b) Is the power generated by Abbie in going up the hill greater than, less than, or the same as the power generated by Bonita in going up the hill?

Explain.

Explanation / Answer

a)

work done does not depend on the path taken but only on the height climbed.

work done = potential energy gained = mgh = weight *height

work done by abbie = 700*30 = 21000 J

work done by bonita= 500*30 = 15000 J

thus work done by abbie > work done by bonita

b)

power = work done/ time

power generated by abbie =21000/60 = 350 W

power generated by bonita = 15000/30 = 500 W

thus power generated by bonita>power generated by abbie

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