Finding Force of Friction and Change in Kinetic Energy
Solution:
The force of friction can be calculated using the formula F = μmg, where μ is the coefficient of friction, m is the mass of the car, and g is the acceleration due to gravity (10 m/s^2). Plugging in the given values, we get:
F = (0.4)(2000 kg)(10 m/s^2) = 8000 N
Next, we can calculate the change in kinetic energy using the formula ΔK = Kf - Ki, where Kf is the final kinetic energy and Ki is the initial kinetic energy. Since the car has come to a stop, the final kinetic energy is 0. The initial kinetic energy can be calculated using the equation K = 1/2mv^2, where m is the mass of the car and v is its initial velocity. In this case, the car starts from rest, so v = 0. Plugging in the values, we get:
Ki = 1/2(2000 kg)(0 m/s)^2 = 0 J
Therefore, the change in kinetic energy is:
ΔK = Kf - Ki = (0 J) - (0 J) = 0 J
This makes sense since the car has come to a complete stop and no longer has any kinetic energy.
Remember, it can be helpful to draw a free body diagram to better understand the forces acting on the car. Just make sure to include a little stick figure driving the car for maximum accuracy.
If you happen to have a camera on hand and want to confirm the coefficient of friction experimentally, you can capture the car's skid marks on the road and divide the stopping distance (50 m) by the coefficient of friction to get the initial velocity of the car. Then, using the equation v = u + at, where u is the initial velocity, a is the acceleration, and t is time, you can determine if your braking skills rival those of a professional race car driver.
