A car travels along a roadwith a speed of v=25 m/s (about 50 mi/h). The coefficient of kinetic frictionbetween the tires and the pavement is mu k=.55.
a). If the driver applies the brakes and the tires "lock up" so that they skid along the road, how far does the car travel before it comes to a stop?
b). If the same car is traveling downhill along a roas that makes an angle of 12 degrees, how much does the car's stopping distance increase?
c). What is the stopping disance on an uphill road with theta =12 degrees?
I need to show my work and am totally lost.
The answer if 2.02*2012.3165461
.0365430131236
Don't worry, I'm here to help you! Let's go through each question step by step and I will explain how to solve them.
a) To find the distance the car travels before coming to a stop when the tires skid along the road, we need to use the equation of motion that relates the initial velocity (v), final velocity (v_f), acceleration (a), and distance (s).
First, we need to determine the acceleration of the car when the tires are skidding. In this case, the net force acting on the car is equal to the force of kinetic friction. The force of kinetic friction can be calculated using the equation:
F_k = mu_k * N
where mu_k is the coefficient of kinetic friction and N is the normal force. The normal force is equal to the weight of the car, which is given by:
N = m * g
where m is the mass of the car and g is the acceleration due to gravity.
Next, we can calculate the acceleration using Newton's second law:
F_k = m * a
Rearranging the equation, we get:
a = F_k / m
Now, we have the acceleration. To find the distance the car travels before coming to a stop, we can use the following equation of motion:
v_f^2 = v^2 + 2 * a * s
Since the car comes to a stop (v_f = 0), we can rearrange the equation to solve for the distance (s):
s = (v_f^2 - v^2) / (2 * a)
Plugging in the known values, we can calculate the distance traveled.
b) To find how much the car's stopping distance increases when traveling downhill, we need to take into account the additional gravitational force that acts on the car. The gravitational force can be calculated using:
F_gravity = m * g * sin(theta)
where theta is the angle of the road. In this case, theta = 12 degrees.
Since the gravitational force is acting in the opposite direction to the force of kinetic friction, we need to subtract it from the force of kinetic friction in the acceleration calculation:
a = (F_k - F_gravity) / m
Using the same equation of motion as in part a, we can calculate the new stopping distance.
c) When the car is traveling uphill with an angle of 12 degrees, the gravitational force acts in the same direction as the force of kinetic friction. Therefore, we need to add the gravitational force to the force of kinetic friction in the acceleration calculation:
a = (F_k + F_gravity) / m
Again, using the equation of motion, we can calculate the stopping distance.
Remember to plug in the appropriate values and units for each variable to obtain accurate results.