A 14560 N car is traveling at 25 m/s. The brakes are applied suddenly, and the car slides to a stop. The average braking force between the tires and the road is 7280 N. How far will the car slide once the brakes are applied? Assume that air resistance is negligible.
Question
A 14560 N car is traveling at 25 m/s. The brakes are applied suddenly, and the car slides to a stop. The average braking force between the tires and the road is 7280 N. How far will the car slide once the brakes are applied? Assume that air resistance is negligible.
Solution
To solve this problem, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
Step 1: Calculate the initial kinetic energy of the car. The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the car and v is its velocity. However, we are given the weight of the car, not its mass. We can find the mass by dividing the weight by the acceleration due to gravity (9.8 m/s^2). So, m = 14560 N / 9.8 m/s^2 = 1485.71 kg. Then, KE_initial = 1/2 * 1485.71 kg * (25 m/s)^2 = 463,677.08 Joules.
Step 2: The final kinetic energy of the car is zero, because the car comes to a stop.
Step 3: The work done on the car is equal to the change in its kinetic energy. So, Work = KE_final - KE_initial = 0 - 463,677.08 J = -463,677.08 Joules. The work is negative because the force is acting in the opposite direction of the car's motion.
Step 4: The work done on the car is also equal to the force applied times the distance over which the force is applied. So, Work = Force * Distance. We can solve for Distance: Distance = Work / Force = -463,677.08 J / 7280 N = -63.7 m.
The negative sign indicates that the distance is in the opposite direction of the initial motion of the car, which makes sense because the car is sliding to a stop. So, the car will slide about 63.7 meters after the brakes are applied.
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