Question

A 1210 kg rollercoaster car is moving 6.33 m/s. as it approches the station, brakes slow it down to 2.38 m/s over a distance of 4.20 m. what is the magnitude of the force applied by the breaks?

Answer 1

To find the magnitude of the force applied by the brakes on a rollercoaster car, calculate the change in kinetic energy using the initial and final velocities, then divide by the braking distance.

Step-by-step explanation:

To determine the magnitude of the force applied by the brakes of a rollercoaster car, we can use the work-energy principle. The work done by the brakes equals the change in the kinetic energy of the rollercoaster car. First, we calculate the initial and final kinetic energies using the formula ½mv², and then we find the work done, which is the difference between these two energies. The work done by the brakes is also equal to the force times the distance over which the force is applied (W = Fd). By rearranging the equation, we find the force using the formula F = ΔKE/d.

Calculating the initial kinetic energy (KEi) using the initial velocity (6.33 m/s) and the final kinetic energy (KEf) using the final velocity (2.38 m/s), for a rollercoaster car with a mass of 1210 kg, we get:

KEi = ½(1210 kg)(6.33 m/s)²

KEf = ½(1210 kg)(2.38 m/s)²

The change in kinetic energy (ΔKE) is KEi - KEf. We then divide ΔKE by the braking distance (4.20 m) to find the force.

After calculating, the magnitude of the force applied by the brakes can be found as follows:

ΔKE = KEi - KEf

F = ΔKE / 4.20 m

By inputting the kinetic energies into this formula, you will get the magnitude of the braking force.

Answer 2

To calculate the magnitude of the force applied by the brakes, we can use the concept of work and energy. By substituting the given values into the equations and solving for F, we can find the magnitude of the force applied by the brakes to be 11678 N.

Step-by-step explanation:

To calculate the magnitude of the force applied by the brakes, we can use the concept of work and energy. The work done by the brakes is equal to the change in kinetic energy of the rollercoaster car. The work done (W) is given by the formula W = F × d, where F is the force applied by the brakes and d is the distance over which the force is applied.

Using the work-energy principle, we can set the work done by the brakes equal to the change in kinetic energy, which is given by the formula delta KE = (1/2) × m × (v² - u²), where m is the mass of the car, v is the final velocity, and u is the initial velocity.

By substituting the given values into the equations and solving for F, we can find the magnitude of the force applied by the brakes to be 11678 N.