A 1580 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 50.0 m?
Calculate the kinetic energy:
E_{k} = 1/2 m v^2
Then use that The work performed by the force must dissipate the kinetic energy. The performed work is force times the distance of 50 m. So, you equate that to E_{k} and solve for the force.
3560 n
To solve this problem, we can use the concept of work and kinetic energy.
Step 1: Calculate the kinetic energy of the car.
The kinetic energy (E_k) of an object is given by the formula E_k = 1/2 m v^2, where m is the mass of the object and v is its velocity.
Given that the mass of the car is 1580 kg and the velocity is 15.0 m/s, we can plug these values into the formula:
E_k = 1/2 (1580 kg) (15.0 m/s)^2
= 1/2 (1580 kg) (225.0 m^2/s^2)
= 1/2 (355500 kg m^2/s^2)
= 177750 J
Step 2: Determine the net force required to bring the car to a halt.
When the car comes to a halt, all of its kinetic energy is dissipated as work done by the net force acting on it. The work done by a force is given by the formula W = Fd, where F is the magnitude of the force and d is the distance over which the force acts.
We are given that the car comes to a halt in a distance of 50.0 m. So, the work done can be calculated as:
W = F(50.0 m)
Since the work done is equal to the kinetic energy, we can set up the following equation:
F(50.0 m) = 177750 J
Solving for F, the magnitude of the net force:
F = 177750 J / 50.0 m
≈ 3550 N
Therefore, the magnitude of the horizontal net force required to bring the car to a halt in a distance of 50.0 m is approximately 3550 N.