2) A car traveling with 5 m/s encounters a deer. The drivers slams on the breaks, the breaks lock. The car
skids to a complete stop on the road ahead (and the deer runs away). Why does the car stop (where does
all the kinetic energy it had go)? Find the magnitude of the friction force if the skid marks show a 20 m slide
and the mass of the car mass is 400 kg.
Here
2a. All KE was converted to PE during braking.
2b. a = (V^2-Vo^2)/2d.
a = (0-(5)^2) / 40 = -0.625 m/s^2.
Wc = mg = 400kg * 9.8N/kg = 3920 N. = Wt. of car
Fc = 3920N @ 0 Deg. = Force of car.
Fp = 3920*sin(0) = 0 = Force parallel to road.
Fv = 3920*cos(0) = 3920N. = Force perpendicular to road.
Fn = Fp - Fk = ma.
0 - Fk = 400*(-0.625).
Fk = 250 N. = Force of kineti friction.
The car stops because of the friction force between the tires and the road. When the driver slams on the brakes and the brakes lock, the friction force between the tires and the road increases. This friction force acts in the opposite direction to the motion of the car, causing it to slow down and eventually come to a stop.
The kinetic energy of the car is converted into other forms of energy during the process of slowing down and stopping. In this case, the kinetic energy is converted into heat through the friction between the tires and the road. The heat is generated due to the interaction between the rubber of the tires and the rough surface of the road. This heat energy is dissipated into the surroundings.
To find the magnitude of the friction force, we can use the concept of work-energy theorem. According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy.
In this case, the work done on the car by the friction force is equal to the change in its kinetic energy. Since the car comes to a complete stop, its final kinetic energy is zero.
So, the work done by the friction force is:
Work = Change in Kinetic Energy
= Kinetic Energy (initial) - Kinetic Energy (final)
= (1/2) * mass * velocity^2 - 0
= (1/2) * 400 kg * (5 m/s)^2
= 5000 J
The work done by the friction force is equal to the product of the magnitude of the friction force and the distance over which the force acts. In this case, the distance is given as 20 m.
So, the magnitude of the friction force can be calculated as:
Work = Force * Distance
5000 J = Force * 20 m
Therefore, the magnitude of the friction force is:
Force = 5000 J / 20 m
= 250 N
Hence, the magnitude of the friction force is 250 Newtons.