you are traveling in your car at a velocity of 24.0 m/s east when you slam on your brakes. The force of friction on your car tires is 1.80x10^4 N. If the mass of you and your car is 1.50x10^3 kg, how far do you skid before stopping?
Until work done against friction equals initial kinetic energy.
To find the distance you skid before stopping, you can use the kinematic equation:
Vf^2 = Vi^2 + 2ad
Where:
Vf = Final velocity (which is 0 m/s because you come to a stop)
Vi = Initial velocity (24.0 m/s east)
a = Acceleration (in this case, the force of friction)
d = Distance
Rearranging the equation to solve for "d", we get:
d = (Vf^2 - Vi^2) / (2a)
Plugging in the values:
d = (0^2 - (24.0 m/s)^2) / (2 * 1.80 * 10^4 N)
Now, let's solve for the distance "d":
To find how far you skid before stopping, we can use the equations of motion.
The first step is to find the acceleration (a) of the car. We can use Newton's second law, which states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), or F = m * a. In this case, the force of friction is acting against the forward motion of the car, so we can write the equation as F = -m * a (negative sign to indicate opposite direction).
Rearranging the equation, we have a = F / m.
Given:
Force (F) = 1.80 x 10^4 N
Mass (m) = 1.50 x 10^3 kg
Substituting these values into the equation, we get:
a = (1.80 x 10^4 N) / (1.50 x 10^3 kg)
Calculating the value of acceleration (a), we find:
a = 12.0 m/s^2
Now, we can use another equation of motion to find the distance (d) traveled during deceleration.
The equation is: v^2 = u^2 + 2ad, where v is the final velocity (0 m/s in this case), u is the initial velocity (24.0 m/s east), a is the acceleration, and d is the distance.
Rearranging the equation, we have d = (v^2 - u^2) / (2a).
Given:
Initial velocity (u) = 24.0 m/s
Final velocity (v) = 0 m/s
Acceleration (a) = -12.0 m/s^2 (negative sign to indicate deceleration)
Substituting these values into the equation, we get:
d = (0^2 - 24.0^2) / (2 * -12.0)
Calculating the value of distance (d), we find:
d = 96.0 meters
Therefore, you would skid approximately 96.0 meters before stopping.