With brakes fully applied, a 1370 kg car deccelerates from a speed of 98.0 km/hr. What is the work done by the braking force in bringing the car to a stop?
Initial speed = 98 km/h = 98/3.6 m/s
Work done
= KE(final)-KE(initial)
= (1/2)1370(0²-(98/3.6)²)
= -508 kJ (approx.)
To calculate the work done by the braking force, we need to use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
To find the work done, we need the initial and final kinetic energies of the car. The initial kinetic energy can be calculated using the formula:
KE_initial = (1/2) * mass * initial_velocity^2
where mass is the mass of the car (1370 kg) and initial_velocity is the initial speed of the car (98.0 km/hr). However, we need to convert the initial velocity from km/hr to m/s.
1 km/hr = 1/3.6 m/s
So, the initial velocity in m/s is:
initial_velocity = 98.0 km/hr * (1/3.6 m/s)/(1 km/hr) = 27.2 m/s
Now, we can calculate the initial kinetic energy:
KE_initial = (1/2) * 1370 kg * (27.2 m/s)^2 = 2210508 J
Since the car comes to a stop, the final kinetic energy is zero. Therefore, the change in kinetic energy is:
change_in_KE = KE_final - KE_initial = 0 - 2210508 J = -2210508 J
The negative sign indicates that work is done on the car in the opposite direction of its motion. Thus, the work done by the braking force in bringing the car to a stop is 2210508 J.
To calculate the work done by the braking force, we need to use the equation:
Work = Force x Distance
Step 1: Convert the speed from km/hr to m/s.
v = 98.0 km/hr = (98.0 * 1000) / (60 * 60) = 27.22 m/s
Step 2: Calculate the deceleration (negative acceleration) using the formula:
v^2 = u^2 + 2as
where v = final velocity, u = initial velocity, a = acceleration, and s = distance.
Rearranging the formula, we get:
a = (v^2 - u^2) / 2s
Given that u = 27.22 m/s and v = 0 (as the car comes to a stop), we can calculate the acceleration.
a = (0^2 - 27.22^2) / (2s)
Step 3: Calculate the distance.
We are not given the distance, so let's call it s.
Step 4: Calculate the force required to decelerate the car.
Using Newton's second law, F = ma, where m is the mass of the car (1370 kg) and a is the acceleration calculated in step 2.
F = 1370 kg * a
Step 5: Calculate the work done.
Using the equation Work = Force x Distance, we can substitute the values calculated in previous steps:
Work = (1370 kg * a) * s
The final step is calculating the value of 'a' (acceleration) and substituting it into the equation.
Now you are ready to calculate the work done by the braking force.