At an accident scene on a level road, investigators measure a car's skid mark to be 58 m long. It was a rainy day and the coefficient of friction was estimated to be 0.46. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.
Well, friction force is mg*mu(greek letter)
That has to equal m*a
a=g*mu a=(9.8)(.46)=4.508
Vfinal^2=0=Vinitial^2-2*a*d
solve for Vinitial
Vinitial^2=2ad=2(4.508)(58)=522.928
Vinitial=sqr rt(522.928)=22.86761903m/s
To determine the speed of the car when the driver slammed on the brakes, we can use the principle of conservation of energy and the concept of work done against friction.
First, let's look at the work-energy principle. When the driver slammed on the brakes, the car's initial kinetic energy was converted into work done against friction to slow down the car. The work done against friction can be expressed as:
Work = Force × Distance
The force of friction can be calculated using the equation:
Force of Friction = Normal Force × Coefficient of Friction
In this scenario, the normal force (equal to the weight of the car) is balanced by the upward normal force. So, we can write:
Force of Friction = Weight × Coefficient of Friction
Now, let's find the weight of the car:
Weight = Mass × Acceleration due to Gravity
Assuming the mass of the car is known, we can calculate the weight.
Next, let's substitute the force of friction into the work equation:
Work = (Weight × Coefficient of Friction) × Distance
The work done against friction is equal to the change in kinetic energy:
Work = Δ Kinetic Energy = 0.5 × Mass × (Final Velocity^2 - Initial Velocity^2)
Since the car came to a stop, the final velocity is zero. Therefore, the equation becomes:
Work = 0.5 × Mass × (0^2 - Initial Velocity^2)
Now, equating the two expressions for work, we get:
0.5 × Mass × (0^2 - Initial Velocity^2) = (Weight × Coefficient of Friction) × Distance
Rearranging the equation, we can solve for the initial velocity:
Initial Velocity = sqrt((2 × Weight × Coefficient of Friction × Distance) / Mass)
Plug in the given values:
Coefficient of Friction = 0.46
Distance = 58 m
Now, we also need to know the mass of the car to calculate the initial velocity. Once the mass is known, substitute it into the equation to find the answer.