A 1000kg car is traveling along a level road at 20.00ms, when the brakes are applied long enough to do 50000 J of work.
1) what is the initial kinetic energy of the car?
2) if the car moved 100m while the brakes where applied, what was the average force exerted on the brakes.
In itial KE = (1/2)M V^2
Your 20.00 ms must be 20.00 m/s.
The brakes do not DO work; they absorb heat equal to the work done by the car (on the brakes) while slowing down.
Force x distance = Kinetic energy loss
Solve for the force.
Thank you.
To answer these questions, we need to understand the concepts of kinetic energy, work, and force.
1) The initial kinetic energy of the car can be calculated using the formula:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Given:
Mass (m) = 1000 kg
Velocity (v) = 20.00 m/s
Substituting the values into the formula:
KE = 0.5 * 1000 kg * (20.00 m/s)^2
= 0.5 * 1000 kg * 400.00 m^2/s^2
= 200,000 J
Therefore, the initial kinetic energy of the car is 200,000 Joules.
2) The average force exerted on the brakes can be determined using the work-energy principle. According to the principle:
Work (W) = Change in Kinetic Energy (ΔKE)
Given:
Work (W) = 50,000 J
Distance (d) = 100 m
The work done on an object is equal to the product of force and displacement:
W = Force * Distance
Rearranging the equation:
Force = Work / Distance
Substituting the given values into the equation:
Force = 50,000 J / 100 m
= 500 J/m
Therefore, the average force exerted on the brakes is 500 Newtons per meter.