The (non-conservative) force propelling a 1.40 x 103-kg car up a mountain road does 7.60 x 106 J of work on the car. The car starts from rest at sea level and has a speed of 22.0 m/s at an altitude of 2.50 x 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 non-conservative forces.

This can't be solved without knowing the distance the car travelled.

Fd - mgh - 1/2mv^2 = W lost

To determine the work done on the car by the combined forces of friction and air resistance, we need to find the total work done on the car and subtract the work done by the non-conservative force propelling the car up the mountain road.

The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy. Therefore, we can calculate the work done by the non-conservative forces (friction and air resistance) by subtracting the work done by the propelling force from the total work done on the car.

Given:
Mass of the car (m) = 1.40 x 10^3 kg
Work done by the propelling force (W_propel) = 7.60 x 10^6 J
Initial speed (v_i) = 0 m/s (car starts from rest)
Final speed (v_f) = 22.0 m/s
Change in altitude (Δh) = 2.50 x 10^2 m

Step 1: Calculate the change in potential energy
The change in potential energy is equal to the work done against gravity.
ΔPE = mgh
where m is the mass, g is the acceleration due to gravity, and h is the change in altitude.
ΔPE = (1.40 x 10^3 kg)(9.8 m/s^2)(2.5 x 10^2 m)
ΔPE = 3.43 x 10^6 J

Step 2: Calculate the work done on the car (W_total)
The total work done on the car is equal to the change in kinetic energy.
W_total = ΔKE = (1/2)mv_f^2 - (1/2)mv_i^2
W_total = (1/2)(1.40 x 10^3 kg)(22.0 m/s)^2 - (1/2)(1.40 x 10^3 kg)(0 m/s)^2
W_total = 6.05 x 10^5 J

Step 3: Calculate the work done by the combined forces (W_friction_air)
W_friction_air = W_total - W_propel
W_friction_air = 6.05 x 10^5 J - 7.60 x 10^6 J
W_friction_air = -7.00 x 10^6 J

Therefore, the work done on the car by the combined forces of friction and air resistance is -7.00 x 10^6 J. The negative sign indicates that these forces are doing work in the opposite direction to the motion of the car, i.e., they are acting to slow down the car.

To find the work done on the car by the combined forces of friction and air resistance, we need to determine the work done by the non-conservative force that is propelling the car up the mountain road first.

Given:
Mass of the car (m) = 1.40 x 10^3 kg
Work done by the non-conservative force (W_nc) = 7.60 x 10^6 J
Initial speed of the car (v1) = 0 m/s (starting from rest)
Final speed of the car (v2) = 22.0 m/s
Change in altitude (h) = 2.50 x 10^2 m

Work done by the non-conservative force (W_nc) can be calculated using the work-energy principle:

W_nc = ΔK + ΔU

where:
ΔK = change in kinetic energy of the car
ΔU = change in potential energy of the car

Since the car starts from rest, the initial kinetic energy is zero, so ΔK = 1/2 * m * (v2^2 - v1^2) = 1/2 * 1.40 x 10^3 kg * (22.0 m/s)^2.

Since the car moves vertically, the potential energy change is given by ΔU = m * g * h, where g is the acceleration due to gravity.

Now, let's calculate the work done by the non-conservative force:

W_nc = ΔK + ΔU
7.60 x 10^6 J = 1/2 * 1.40 x 10^3 kg * (22.0 m/s)^2 + 1.40 x 10^3 kg * g * (2.50 x 10^2 m)

From this equation, we can solve for g, which is the acceleration due to gravity.

First, simplify the equation:

7.60 x 10^6 J = 1/2 * 1.40 x 10^3 kg * (22.0 m/s)^2 + 1.40 x 10^3 kg * g * (2.50 x 10^2 m)

Now, isolate g:

7.60 x 10^6 J - 1/2 * 1.40 x 10^3 kg * (22.0 m/s)^2 = 1.40 x 10^3 kg * g * (2.50 x 10^2 m)

Finally, divide both sides by 1.40 x 10^3 kg * (2.50 x 10^2 m) to solve for g:

g = (7.60 x 10^6 J - 1/2 * 1.40 x 10^3 kg * (22.0 m/s)^2) / (1.40 x 10^3 kg * (2.50 x 10^2 m))

Now that we have the value of g, we can calculate the work done by the combined forces of friction and air resistance.

The work done by friction and air resistance (W_friction) is given by:

W_friction = W_total - W_nc

where W_total is the total work done on the car.

The total work done on the car (W_total) can be calculated if we know the net force acting on the car. However, based on the information provided, we do not have access to the net force or any other information to directly calculate W_total.

Therefore, without additional information, we cannot determine the work done on the car by the combined forces of friction and air resistance.