This question is typical on some driver's license exams: A car moving at 48 km/h skids
13 m with locked brakes.
How far will the car skid with locked brakes at 120 km/h? Assume that energy loss is due only to sliding friction.
Answer in units of m. Answer in units of
ml.
To determine the distance the car will skid with locked brakes at 120 km/h, we need to make use of the concept of kinetic energy and the relationship between kinetic energy and work done by friction. The work done by friction can be found by multiplying the force of friction by the distance the car skids.
First, let's find the initial kinetic energy of the car moving at 48 km/h. The formula for kinetic energy is given as:
Kinetic Energy = (1/2) * mass * velocity^2
Since mass is not given, we can ignore it for now and focus on the comparison between the two speeds.
The initial kinetic energy of the car moving at 48 km/h is:
KE_1 = (1/2) * mass * (48 km/h)^2
Now, we can find the work done by friction using the energy loss due to sliding friction. The energy loss can be calculated as the difference in kinetic energy between the two speeds:
Energy Loss = KE_1 - KE_2
Next, let's determine the final kinetic energy of the car at 120 km/h. The kinetic energy formula can be used again:
KE_2 = (1/2) * mass * (120 km/h)^2
Now we can find the energy loss due to sliding friction:
Energy Loss = (1/2) * mass * (48 km/h)^2 - (1/2) * mass * (120 km/h)^2
Since we are looking for the distance the car skids, we can also define the work done by friction as:
Work done by friction = force of friction * distance
The force of friction is equal to the normal force multiplied by the coefficient of sliding friction. Since the mass cancels out, we can write:
(1/2) * mass * (48 km/h)^2 - (1/2) * mass * (120 km/h)^2 = force of friction * distance
Given that the force of friction is constant, we can rearrange the equation to solve for the distance:
distance = (1/2) * mass * (48 km/h)^2 - (1/2) * mass * (120 km/h)^2 / force of friction
Since we are assuming that energy loss is due only to sliding friction, we can use the same value for the coefficient of sliding friction as in the initial scenario. Therefore:
distance = (1/2) * mass * (48 km/h)^2 - (1/2) * mass * (120 km/h)^2 / force of friction
It is important to note that without information about the mass of the car or the coefficient of sliding friction, it is not possible to determine the exact distance the car will skid at 120 km/h.