With brakes fully applied, a 1660 kg car decelerates from a speed of 74.0 km/hr. What is the work done by the braking force in bringing the car to a stop? What is the change in the kinetic energy of the car?
To find the work done by the braking force in bringing the car to a stop, we can use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
First, let's convert the car's initial speed from km/hr to m/s, as we typically use SI units in physics.
Given:
Mass of the car, m = 1660 kg
Initial speed, v = 74.0 km/hr
Converting from km/hr to m/s:
v = (74.0 km/hr) * (1000 m/km) * (1 hr/3600 s)
v ≈ 20.56 m/s (rounded to two decimal places)
Since the car is decelerating and coming to a stop, its final velocity will be zero.
The change in kinetic energy, ΔK, is given by the formula:
ΔK = 0.5 * m * (vf^2 - vi^2)
Plugging in the known values:
ΔK = 0.5 * 1660 kg * (0 - 20.56 m/s)^2
Simplifying:
ΔK = 0.5 * 1660 kg * (-20.56 m/s)^2
ΔK = 0.5 * 1660 kg * 421.9136 m^2/s^2
ΔK ≈ -348,551 J (rounded to the nearest whole number)
The negative sign indicates that the kinetic energy of the car has decreased.
Now, let's calculate the work done by the braking force using the work-energy principle:
Work done, W = ΔK
Therefore, the work done by the braking force in bringing the car to a stop is approximately -348,551 Joules (J), and the change in kinetic energy of the car is approximately -348,551 Joules (J).