A 1500 kg car moving at 10 m/s is stopped by the action of its brakes. The
work done by the car's brakes is ____ Joules.
Well, let's calculate it, but first, let me put on my imaginary racing helmet. Zoom zoom! 🏎️
To calculate the work done by the brakes, we can use the formula:
Work = Force × Distance
To stop the car, the brakes exert a force on it. The force can be found using Newton's second law:
Force = Mass × Acceleration
Since the car is stopping, its acceleration is in the opposite direction of its velocity (negative). So, the acceleration is:
Acceleration = Change in Velocity / Time
Since the car is coming to a stop, its final velocity is 0 m/s. Therefore:
Acceleration = (0 m/s - 10 m/s) / Time
Now, let's assume the stopping time of the car is 5 seconds for the sake of simplicity. Then:
Acceleration = (-10 m/s) / 5 s
Acceleration = -2 m/s²
After we've got the acceleration, we can calculate the force:
Force = Mass × Acceleration
Force = 1500 kg × (-2 m/s²)
Force = -3000 N
Since the car is stopping, the force exerted by the brakes is in the opposite direction of the car's motion. That's why we have a negative sign here.
Now, to find the work:
Work = Force × Distance
Since the car is coming to a stop, we can say the distance it travels while braking is the same as its initial displacement:
Distance = 10 m
So:
Work = -3000 N × 10 m
Work = -30,000 J
Since work is a scalar quantity, we ignore the negative sign here. Therefore, the work done by the car's brakes is approximately 30,000 Joules.
And that, my friend, concludes our math comedy act for today! Thank you, thank you! 🎉🤡
To find the work done by the car's brakes, we need to use the definition of work, which is given by the equation:
Work = force × distance × cos(θ)
In this case, the force is the force applied by the brakes to stop the car, the distance is the distance over which the car was stopped, and θ is the angle between the force applied by the brakes and the direction of motion of the car (which is 180 degrees in this case).
First, let's calculate the force applied by the brakes. Since the car is stopped, the net force on the car is equal to the force applied by the brakes. According to Newton's second law (F = ma), the force applied by the brakes is given by the equation:
Force = mass × acceleration
Given that the mass of the car is 1500 kg, and the car is stopped (which means its final velocity is 0 m/s), the acceleration can be calculated using the equation:
acceleration = (final velocity - initial velocity) / time
Since the final velocity is 0 m/s and the initial velocity is 10 m/s, and the time taken to stop the car is not given, we cannot calculate the acceleration or force directly with the given information. We need more information about the time or the deceleration rate.
Hence, without additional information, we cannot determine the work done by the car's brakes.
To find the work done by the car's brakes, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy of the car can be calculated using the formula:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the car, and v is its velocity.
Plugging in the given values:
KE_initial = (1/2) * 1500 kg * (10 m/s)^2 = 75,000 J
Since the car is stopped, its final velocity is 0. Therefore, the final kinetic energy is:
KE_final = (1/2) * 1500 kg * (0 m/s)^2 = 0 J
The work done by the car's brakes can be expressed as the change in kinetic energy:
Work = KE_final - KE_initial
= 0 J - 75,000 J
= -75,000 J
Note that the negative sign indicates that the work is done by the brakes to stop the car's motion.
Therefore, the work done by the car's brakes is -75,000 Joules.