Question

You are testing a new amusement park roller coaster with an empty car with a mass of 105 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 it has speed of 8.00 m/s .

Answer 1

To find the speed of the roller coaster at the top of the loop, we can use the principle of conservation of mechanical energy.

Step-by-step explanation:

To find the speed of the roller coaster at the top of the loop, we can use the principle of conservation of mechanical energy. At the bottom of the loop, the roller coaster has a speed of 25.0 m/s and a height of 0 m. At the top of the loop, the roller coaster has a speed of 8.00 m/s and a height of 12.0 m.

Using the equation for conservation of mechanical energy, we have:

mgh + 1/2mv^2 = mgh' + 1/2mv'^2

Where m is the mass of the roller coaster, g is the acceleration due to gravity, h is the initial height, v is the initial velocity, and h' and v' are the final height and velocity.

Plugging in the values, we get:

(105 kg)(9.8 m/s^2)(0 m) + 1/2(105 kg)(25.0 m/s)^2 = (105 kg)(9.8 m/s^2)(12.0 m) + 1/2(105 kg)(v')^2

Simplifying, we find that the final speed of the roller coaster at the top of the loop is 10.0 m/s.