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 . Part A As the car rolls from point A to point B, how much work is done by friction

Answer 1

The work done by friction as the car rolls from point A to point B on the roller coaster can be calculated using the equation Work = force x distance. The force due to friction can be calculated using the equation Force = mass x acceleration. By finding the height difference between point A and B, which is equal to twice the radius of the loop, the distance can be calculated and used in the work equation. The calculated work done by friction is 193075.04 J.

Step-by-step explanation:

Work is done by friction when there is a force acting opposite to the direction of motion. In this case, as the car rolls from point A to point B, the friction force acts in the opposite direction to the motion of the car. The work done by friction can be calculated using the equation:

Work = force x distance

Here, the force due to friction can be calculated using the equation:

Force = mass x acceleration

At point A, the car has a speed of 25.0 m/s. To calculate the acceleration at point A, we can use the centripetal acceleration formula:

Centripetal acceleration = (velocity^2) / radius

Plugging in the values, the centripetal acceleration at point A can be calculated as:

Centripetal acceleration at point A = (25.0 m/s)^2 / 12.0 m = 52.083 m/s^2

The acceleration at point A is the sum of the centripetal acceleration and the acceleration due to gravity:

Total acceleration at point A = 52.083 m/s^2 + 9.8 m/s^2 = 61.883 m/s^2

Now, using the equation Force = mass x acceleration, the force due to friction at point A can be calculated as:

Force at point A = 130 kg x 61.883 m/s^2 = 8044.79 N

The distance between point A and point B can be calculated by finding the height difference between the two points. Since the car is at the bottom of the loop at point A and at the top of the loop at point B, the height difference is equal to twice the radius of the loop:

Distance = 2 x radius = 2 x 12.0 m = 24.0 m

Finally, we can calculate the work done by friction using the equation Work = force x distance:

Work = 8044.79 N x 24.0 m = 193075.04 J