A(n) 1949.1 kg car is coasting along a level road at 22.9 m/s. A constant braking force is applied, such that the car is stopped in a distance of 74.6 m.
What is the magnitude of the braking force? Answer in units of N
a = (V^2-Vo^2)/2d = (0-(22.9^2)/149.2 =
-3.51 m/s^2.
F = m*a =1949.1 * (-3.51) = -6851 N.
Note: The negative sign means that the
force opposes the motion.
To find the magnitude of the braking force, we can use the work-energy principle. The work done by the braking force is equal to the change in kinetic energy of the car.
The work done by the braking force is given by the equation:
Work = Force * Distance
The change in kinetic energy is given by the equation:
Change in Kinetic Energy = 0.5 * mass * (final velocity^2 - initial velocity^2)
Since the car is coasting and eventually stops, the final velocity is 0 m/s.
Substituting the given values into the equations:
Work = Force * Distance
Change in Kinetic Energy = 0.5 * mass * (final velocity^2 - initial velocity^2)
We can equate the two expressions and solve for the magnitude of the braking force:
Force * Distance = 0.5 * mass * (0 - initial velocity^2)
Force = (0.5 * mass * (0 - initial velocity^2)) / Distance
Now, let's substitute the given values:
Force = (0.5 * 1949.1 kg * (0 - (22.9 m/s)^2)) / 74.6 m
Calculating the expression:
Force = (0.5 * 1949.1 kg * (0 - 524.41 m^2/s^2)) / 74.6 m
Force = (0.5 * 1949.1 kg * (-524.41 m^2/s^2)) / 74.6 m
Force = -524.41 N
Since force is a vector quantity and the magnitude of a vector is always positive, the magnitude of the braking force is 524.41 N.
To find the magnitude of the braking force, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the acceleration of the car. The initial velocity is 22.9 m/s, and the final velocity is 0 m/s (since the car is stopped). The distance over which the car is stopped is 74.6 m. We can use the following equation to find the acceleration:
vf^2 = vi^2 + 2ad
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and d is the distance.
Rearranging the equation, we have:
a = (vf^2 - vi^2) / (2d)
Substituting the values we have:
a = (0^2 - 22.9^2) / (2 * 74.6)
a = -532.41 / 149.2
a ≈ -3.57 m/s^2
Since the car is being decelerated (braking), the acceleration has a negative sign.
Now we can find the magnitude of the braking force using Newton's second law:
F = ma
Substituting the values we have:
F = (1949.1 kg) * (-3.57 m/s^2)
F ≈ -6960.207 N (negative because it represents the deceleration)
Thus, the magnitude of the braking force is approximately 6960.207 N.