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Answer :
A car is moving across a level highway with a speed of 22.9 m/s. The brakes are applied and the wheels become locked as the 1260-kg car skids to a stop. The braking distance is 126 meters.
Velocity of car, v = 22.9 m/s Mass of car, m = 1260 kg Braking distance, s = 126 m
The initial energy of the car can be calculated as:
Initial Kinetic Energy of the car = 1/2 mv²
Here, m = 1260 kg, v = 22.9 m/s
Putting these values in the above formula: Initial Kinetic Energy = 1/2 × 1260 kg × (22.9 m/s)²= 1/2 × 1260 kg × 524.41 m²/s²= 165748.1 J
The final energy of the car is zero as the car is at rest now. Work done by the brakes to stop the car can be calculated as follows:
Work Done = Change in Kinetic Energy= Final Kinetic Energy - Initial Kinetic Energy
The final kinetic energy of the car is zero. Therefore, Work Done = 0 - 165748.1 J= -165748.1 J (Negative sign indicates the energy is lost by the car during the application of brakes)
The magnitude of the braking force acting upon the car can be calculated using the work-energy principle. The work done by the brakes is equal to the net work done by the forces acting on the car. Therefore,
Work Done by Brakes = Force x Distance
The frictional force acting on the car is equal to the force applied by the brakes. Hence,
Force = Frictional force acting on the car. The work done by the frictional force can be calculated as follows:
Work Done = Frictional force x Distance
Therefore, Frictional force acting on the car = Work Done / Distance= -165748.1 J / 126 m= -1314.6 N (The negative sign indicates that the force acts opposite to the direction of motion of the car. The magnitude of the force is 1314.6 N.)
Therefore, Initial Energy of the car = 165748.1 J
Final Energy of the car = 0 J
Work done by the brakes to stop the car = -165748.1 J
Magnitude of the braking force acting upon the car = 1314.6 N
Learn more about Kinetic energy: https://brainly.com/question/8101588
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