The driver of a 1300 kg car, initially traveling at 10.1 m/s, applies the brakes, bringing the car to rest in a distance of 16.5 m.
(a) Find the net work done on the car.
(b) Find the magnitude and direction of the force that does this work. (Assume this force is constant.)
magnitude
To find the net work done on the car, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy of the car is given by the formula:
KE_initial = (1/2) * mass * velocity^2
Substituting the given values:
mass = 1300 kg
velocity = 10.1 m/s
KE_initial = (1/2) * 1300 kg * (10.1 m/s)^2
Next, we need to find the final kinetic energy of the car. Since the car comes to rest, the final kinetic energy is zero:
KE_final = 0
The net work done on the car is equal to the change in kinetic energy:
Net work = KE_final - KE_initial
Substituting the values:
Net work = 0 - [(1/2) * 1300 kg * (10.1 m/s)^2]
Now we can calculate the net work done on the car.
(b) To find the magnitude and direction of the force that does this work, we can use the formula for work:
Work = force * distance * cos(theta)
where theta is the angle between the force and the displacement. In this case, the force is in the opposite direction of the displacement, so theta is 180 degrees.
The work done on the car is equal to the net work we calculated in part (a):
Net work = force * distance * cos(180 degrees)
Simplifying the expression:
Net work = -force * distance
Now we can solve for the force:
-force * distance = Net work
force = -Net work / distance
Substituting the values:
Net work = calculated in part (a)
distance = 16.5 m
Now we can calculate the magnitude of the force.