A car of mass 1120 kg descends a hill of slope 1 in 5.calculate using the energy theory methods the average braking force required to bring the car to rest from 20m/s in 60m,assume the frictional resistance is 260N
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To calculate the average braking force required to bring the car to rest from a given velocity using energy theory methods, we need to consider the change in kinetic energy and the work done by friction.
First, let's calculate the change in kinetic energy. The initial kinetic energy (KE1) is given by:
KE1 = (1/2) * mass * (initial velocity)^2
KE1 = (1/2) * 1120 kg * (20 m/s)^2
KE1 = 1120 * 200 J
KE1 = 224000 J
The final kinetic energy (KE2) is zero since the car comes to rest.
Next, let's calculate the work done by friction. The work done by a force is given by:
Work = force * distance
In this case, the distance is given as 60 m, and the frictional resistance force is given as 260 N.
Work = 260 N * 60 m
Work = 15600 J
Since the work done by friction opposes motion, it is negative. Therefore, the work done by friction is -15600 J.
Now, using the principle of energy conservation, the change in kinetic energy is equal to the negative work done by friction.
KE2 - KE1 = -Work
0 - 224000 J = -(-15600 J)
224000 J = 15600 J
Now, let's calculate the average braking force required to bring the car to rest. The average braking force is given by:
Average Force = Work / distance
Average Force = (-15600 J) / 60 m
Average Force = -260 N
Note that the average force is negative, indicating that it acts in the opposite direction of the car's motion (braking force).
Therefore, the average braking force required to bring the car to rest is -260 N.