Question

You are testing a new amusement park roller coaster with an empty car with a mass of 130 kg. One part of the track is a vertical loop with a radius of 12.0 m. At the bottom of the loop (point A) the car has a speed of 25.0 m/s and at the top of the loop (point B) it has speed of 8.00 m/s.

Answer 1

Answer:

Work done by friction along the motion is given as

$W_f = -5857.8 J$

Explanation:

As per work energy theorem we can say

Work done by all forces = change in kinetic energy of the system

so here car is moving from bottom to top

so here the change in kinetic energy is total work done on the car

so here we will have

$W_f + W_g = \frac{1}{2}m(v_f^2 - v_i^2)$

$W_f - mgH = \frac{1}{2}m(v_f^2 - v_i^2)$

now plug in all data in it

$W_f - (130)(9.81)(2\times 12) = \frac{1}{2}(130)(8^2 - 25^2)$

$W_f = 30607.2 - 36465$

$W_f = -5857.8 J$