car doing 60 mph and skids for 52.3 meters what is the speed at end of skid co/friction is 0.693 urgent help please
To find the speed of the car at the end of the skid, we can use the concept of work and energy. The work done on the car by the friction force is equal to the change in kinetic energy of the car.
The work done by the friction force is given by:
Work = Force × Distance × cos(theta)
In this case, the force is the frictional force, which is given by the coefficient of friction (µ) multiplied by the normal force (N), where N = mass × gravity. The distance is the skid distance, and theta is the angle between the force and distance vectors, which is 0 degrees in this case (cos(0) = 1).
So, the work done can be written as:
Work = µ × N × Distance
Since the work done is equal to the change in kinetic energy, we can write:
Work = (1/2) × mass × (v_final^2 - v_initial^2)
Where v_final is the final velocity and v_initial is the initial velocity of the car.
Now, we can equate the two equations and solve for v_final:
µ × N × Distance = (1/2) × mass × (v_final^2 - v_initial^2)
Given that the initial velocity (v_initial) is 60 mph, we need to convert it to meters per second (m/s) by multiplying by 0.44704:
v_initial = 60 mph × 0.44704 m/s per mph = 26.8224 m/s
Given the coefficient of friction (µ) is 0.693, the skid distance (Distance) is 52.3 meters, and assuming the mass of the car is known, we can calculate the final velocity (v_final).