A 1370 kg car is traveling with a speed of 15.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 49.5 m?
To find the magnitude of the horizontal net force required to bring the car to a halt, we can use the equations of motion.
First, let's write down the given information:
Mass of the car (m) = 1370 kg
Initial velocity (v) = 15.0 m/s
Stopping distance (d) = 49.5 m
We'll use the equation of motion that relates velocity, initial velocity, acceleration, and distance:
v^2 = u^2 + 2ad
Here, v is the final velocity (zero since the car is brought to a halt), u is the initial velocity, a is the acceleration, and d is the distance.
Rearranging the equation, we have:
2ad = -u^2
Since the final velocity is zero, we can substitute 0 for v:
2a(49.5 m) = -(15.0 m/s)^2
Simplifying:
a = -[(15.0 m/s)^2] / (2 × 49.5 m)
a ≈ -7.65 m/s^2
The negative sign indicates that the acceleration acts in the opposite direction to the motion of the car. In this case, since the car is brought to a halt, the acceleration will be directed against the car's motion.
Next, we can calculate the net force acting on the car using Newton's second law:
F = m × a
F = (1370 kg) × (-7.65 m/s^2)
F ≈ -10515 N
The magnitude of the force is obtained by taking the absolute value of the calculated force:
|F| ≈ 10515 N
Therefore, the magnitude of the horizontal net force required to bring the car to a halt in a distance of 49.5 m is approximately 10515 N.