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, we need to calculate the force applied by the brakes first.
To calculate the force, we will use the equation:
Force = mass x acceleration
Since the car is decelerating, the acceleration is the negative of the deceleration.
1. Convert the speed from km/hr to m/s:
Speed = 74.0 km/hr
Speed = 74.0 x (1000/3600) = 20.6 m/s
2. Calculate the deceleration using the formula:
Deceleration = (final velocity - initial velocity) / time
Since the car is brought to a stop, the final velocity is 0 m/s:
Deceleration = (0 - 20.6) / t
Let's assume the time taken to bring the car to a stop is t seconds.
3. Now, we will calculate the force applied:
Force = mass x acceleration
Force = 1660 kg x deceleration
To calculate the work done by the braking force, we use the equation:
Work = force x distance
Since the car is brought to a stop, the distance covered is the same as the braking distance. However, the distance is not mentioned in the question. Hence, we cannot calculate the work done by the braking force without knowing the braking distance.
Now, let's move on to calculating the change in the kinetic energy of the car.
The change in kinetic energy can be calculated using the equation:
Change in kinetic energy = 0.5 x mass x (final velocity^2 - initial velocity^2)
Since the car is brought to a stop, the final velocity is 0 m/s.
Change in kinetic energy = 0.5 x 1660 kg x (0 - 20.6^2)
Change in kinetic energy = 0.5 x 1660 kg x (-423.16)
Change in kinetic energy = -139,987.36 J
Hence, the change in kinetic energy of the car is -139,987.36 J.
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 done is equal to the change in kinetic energy.
First, let's convert the speed of the car from km/hr to m/s. We can use the conversion factor 1 km/hr = 1000 m/3600 s.
Speed of the car = 74.0 km/hr * (1000 m/3600 s) = 20.56 m/s
Now, let's calculate the initial kinetic energy of the car using the formula:
Kinetic energy = 1/2 * mass * velocity^2
Mass of the car = 1660 kg
Initial kinetic energy = 1/2 * 1660 kg * (20.56 m/s)^2 = 340,944.32 J
Since the car comes to a stop, the final kinetic energy is zero.
The change in kinetic energy is the difference between the final kinetic energy (0 J) and the initial kinetic energy (340,944.32 J):
Change in kinetic energy = 0 J - 340,944.32 J = -340,944.32 J
Therefore, the change in kinetic energy of the car is -340,944.32 J.
Since the work done by the braking force is equal to the change in kinetic energy, the work done is also -340,944.32 J.