The (nonconservative) force propelling a 1.50 103-kg car up a mountain road does 5.10 106 J of work on the car. The car starts from rest at sea level and has a speed of 31.5 m/s at an altitude of 1.90 102 m above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are nonconservative forces.
work done by friction= workinput-realenergyoutput
work done by friction= 5E6J-1/2 m 31.5^5-mg(190)
To find the work done on the car by the combined forces of friction and air resistance, we can use the work-energy theorem.
According to the work-energy theorem, the net work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy of the car is given by KE_initial = (1/2) * m * v_initial^2, where m is the mass of the car and v_initial is the initial velocity of the car.
The final kinetic energy of the car is given by KE_final = (1/2) * m * v_final^2, where v_final is the final velocity of the car.
The net work done on the car can be calculated as the difference between the final and initial kinetic energies, W_net = KE_final - KE_initial.
Given:
Mass of the car, m = 1.50 * 10^3 kg
Initial velocity, v_initial = 0 m/s (since the car starts from rest)
Final velocity, v_final = 31.5 m/s
Change in altitude, h = 1.90 * 10^2 m
Using the formula for gravitational potential energy, the change in potential energy is given by PE_change = m * g * h, where g is the acceleration due to gravity.
Substituting the given values, PE_change = (1.50 * 10^3 kg) * (9.8 m/s^2) * (1.90 * 10^2 m).
The work done by the non-conservative forces (friction and air resistance) is equal to the net work done on the car minus the change in potential energy caused by gravity:
W_non-conservative = W_net - PE_change.
First, we need to calculate the initial kinetic energy and work:
KE_initial = 0 (since the car starts from rest)
W_initial = KE_final - KE_initial = (1/2) * m * v_final^2 - 0 = (1/2) * (1.50 * 10^3 kg) * (31.5 m/s)^2.
Now we can calculate the work done by the non-conservative forces:
W_non-conservative = W_initial - PE_change.
Substituting the given values and solving the equation, we can find the work done by the combined forces of friction and air resistance.
To obtain the work done on the car by the combined forces of friction and air resistance, we need to calculate the work done by the nonconservative force propelling the car up the mountain road and subtract it from the total work done on the car.
First, let's calculate the work done by the nonconservative force propelling the car up the mountain road. We are given that this force does 5.10 * 10^6 J of work on the car.
Next, we need to calculate the total work done on the car. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Since the car starts from rest, its initial kinetic energy is zero.
The final kinetic energy of the car can be calculated using the equation:
KE = (1/2) * m * v^2
where m is the mass of the car and v is its final velocity.
So, the final kinetic energy of the car is:
KE = (1/2) * (1.50 * 10^3 kg) * (31.5 m/s)^2
Next, we can calculate the total work done on the car:
Total work done = KE - Initial kinetic energy
Total work done = KE - 0
Now, the work done on the car by the combined force of friction and air resistance can be calculated by subtracting the work done by the nonconservative force from the total work done on the car:
Work done by combined forces = Total work done - Work done by nonconservative force
Substituting the given values into the equation, we can solve for the work done by the combined forces.