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.
W(fr)=KE2-KE1=
= 0- mv²/2= - 1500•10²/2= - 75000 J.
To calculate the work done by the car's brakes, we need to use the formula:
Work = Force × Distance
First, let's calculate the force exerted by the car's brakes. The force needed to stop the car can be calculated using Newton's second law:
Force = mass × acceleration
In this case, the acceleration is the change in velocity over time. Since the car comes to a stop, the final velocity is 0 m/s, and the initial velocity is 10 m/s. Let's calculate the acceleration:
Change in velocity = final velocity - initial velocity
Change in velocity = 0 m/s - 10 m/s = -10 m/s
Therefore, the acceleration is -10 m/s divided by the time it takes for the car to stop, which is not mentioned in the given information.
Now, let's calculate the force exerted by the brakes by using the formula:
Force = mass × acceleration
Force = 1500 kg × acceleration
Without the value of acceleration, we cannot accurately calculate the force or the work done by the car's brakes.
To find the work done by the car's brakes, we can use the formula for work:
Work = Force x Distance
In this case, the force applied by the brakes is responsible for stopping the car, and it acts over a certain distance. The force can be calculated using Newton's second law:
Force = Mass x Acceleration
Given that the mass of the car is 1500 kg and it is brought to a stop from a velocity of 10 m/s, we can calculate the acceleration using the equation:
Final Velocity^2 = Initial Velocity^2 + 2 x Acceleration x Distance
Rearranging the equation, we get:
Acceleration = (Final Velocity^2 - Initial Velocity^2) / (2 x Distance)
Since the final velocity is 0 m/s (as the car is brought to a stop), the equation simplifies to:
Acceleration = - (Initial Velocity^2) / (2 x Distance)
Substituting the values, we have:
Acceleration = - (10^2) / (2 x Distance)
Now, let's solve for the distance. Rearranging the equation, we find:
Distance = - (10^2) / (2 x Acceleration)
Since we know that the force applied by the brakes is responsible for stopping the car, the acceleration is equal to the force divided by the mass:
Acceleration = Force / Mass
Simplifying further, we have:
Distance = - (10^2) / (2 x (Force / Mass))
Multiplying both sides by -1 to get a positive distance, we get:
Distance = (10^2) x (Mass / (2 x Force))
Finally, substitute the values to find the distance traveled:
Distance = (10^2) x (1500 / (2 x Force))
Now, we can substitute the obtained distance back into the formula for work:
Work = Force x Distance
Given that the force applied by the brakes is the same as the force required to bring the car to a stop, we can now evaluate the work done by the car's brakes.