You have been ask to evaluate the effect of frictional forces on the energy of s

Question

You have been ask to evaluate the effect of frictional forces on the energy of some cars which might be chosen for a new amusement park roller coaster. You are making some test runs with an empty car with a mass of 100.0 kg . One part of the track is a circular vertical loop with a radius of 12.3 m . In one of your tests, at the bottom of the loop (point A) the car has a measured speed of 26.5 m/s and at the top of the loop (point B) it has a measured speed of 7.30 m/s .

A. As the car rolls from point A to point B, how much work is done by the normal force on the car by the track?

B. As the car rolls from point A to point B, what is the net work done on the car?

C. As the car rolls from point A to point B, how much work has been done on the car by friction?

Explanation / Answer

A)

the work done by the normal force is zero because the car is moving in a direction perpendicular to the normal force

B)

and the work done on car from Ato B is gravitational energy which W=m(-g)(2h) since the lenth 2h is diameter the distance between A and B

-100*9.8*24.6

= -24108 Jas h=12.3 m

C)

now final velocity isV= 7.3 m/s and initail isU= 26.5m/s

the distnce travelled from A to B is semi cicrlce distnce which is 3.14*12.3=38.622m

V^2-U^2=2aS

now a is negative as friction is opposite to the direction of motion

(7.3)^2-(26.5)^2=a77.24

a= -8.4m/s

frictionla force is given by

F=ma=100*-8.4=-840 N

work done by this force to take fromA to B

is W=F.S

=-840*77.24=-64896 J

work done by fricional foce is -64896 J

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