A 1500-kg wooden roller coaster car traveling at 15 m/s approaches the loading station where the under-track brake strips are pneumatically actuated to slow the car to a stop in 10m. What is the work done on the car by the brakes? What is the retarding force (friction) the car experiences?
if anyone could help that would be great!
This is just like your last problem but reversed.
initial Ke = (1/2) m v^2 = (1/2)(1500) (225) Joules
that is the work done by the brakes (negative)
Final Ke - initial Ke = work in
Final is 0, initial is above ( 750)(225) so 0 - 168750 Joules
Force of brakes * 10 meters = work done by brakes (which is negative of course, force opposite to motion)
To find the work done on the car by the brakes, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy. The formula for work is given by:
Work = Force x Distance x Cos(θ)
where Force is the applied force by the brakes, Distance is the distance over which the force is applied, and θ is the angle between the force and the direction of motion.
In this case, the car is being slowed down, so the θ would be 180 degrees (opposite direction to the motion). The work done by the brakes is equal to the negative of the change in kinetic energy.
First, let's calculate the initial kinetic energy (Ki) of the car:
Ki = 1/2 x mass x velocity^2
= 1/2 x 1500 kg x (15 m/s)^2
Next, let's calculate the final kinetic energy (Kf) of the car, when it comes to a stop:
Kf = 0 (when the car is at a stop, its kinetic energy is 0)
Now, we can find the change in kinetic energy:
ΔK = Kf - Ki
= 0 - [1/2 x 1500 kg x (15 m/s)^2]
Finally, the work done by the brakes is equal to the negative of the change in kinetic energy:
Work = - ΔK
To find the retarding force (friction) experienced by the car, we can use Newton's second law of motion:
Force = mass x acceleration
In this case, the acceleration is the rate at which the car's velocity changes over time due to the braking force applied by the brakes. We can calculate the deceleration (negative acceleration) using the formula:
Deceleration = (final velocity - initial velocity) / time
Now, substituting the values given:
Deceleration = (0 m/s - 15 m/s) / 10 m
Finally, the retarding force (friction) experienced by the car is given by:
Force = mass x deceleration
Substituting the values:
Force = 1500 kg x Deceleration
Now, you can plug in the values in the above formulas and calculate the work done by the brakes and the retarding force experienced by the car.