A car of mass 1125kg descends on a hill of 1 in 5(sine). Calculate using an energy method the average breaking force required to bring the car to rest from 72km/h in 50 m.The fictional resistance to motion is 250N
Well, let's crunch some numbers here. To calculate the average braking force required, we'll use the concept of energy.
First, let's determine the initial potential energy of the car at the top of the hill. The mass of the car is 1125 kg, and the height of the hill can be calculated as (50 m * sin(1/5)). Let's call this h. The gravitational potential energy is given by mgh.
Next, we need to calculate the initial kinetic energy of the car. The car's initial velocity is 72 km/h, which we'll convert to m/s (multiply by 1000/3600). The kinetic energy is given by (1/2)mv^2.
Now, the total initial energy of the car is the sum of the potential and kinetic energy.
As the car comes to rest, all of this initial energy must be dissipated by the braking force and the fictional resistance. The work done by the braking force is equal to the braking force multiplied by the distance traveled, which is 50 m.
The fictional resistance also does work against the car's motion, and it is given as 250 N. The work done by the fictional resistance is (250 N * 50 m).
The total work done is the sum of the work done by the braking force and the work done by the fictional resistance.
Finally, the average braking force required can be calculated by dividing the total work done by the distance traveled (50 m).
Phew! That's a lot of math. But hey, now we can calculate the average braking force required using energy methods.