The (nonconservative) force propelling a 1.50E3 kg car up a mountain road does 4.70E6 j of work on the car. The car starts from rest at sea level and has a speed of 27.0 m/s at an altitude of 2.00E2 m above sea level. Obtain the work done on the car by the combined forces of friction and air resitstance, both of which are nonconservative forces.

This is Chapter 6, Work and Energy, of Physics, 8th Edition, by Cutnell, #55.

I know it has something to do with initial and final energies being equal.

I also know that kinetic and gravitational potential are the only two energies involved.

I got this from Answers:

Total Energy (at end) = KE + PE

So set this equal to Wdone - Wdiss

Wdiss = Wdone - KE - PE
Wdone = 4.7e6 J
KE = (1/2)mv^2
PE = mgh
m = 1.5e3 kg
v = 27 m/s
h = 2e2 m

Wdiss = 4.7e6 - .5 * 1.5e3 * 27^2 - 1.5e3 * 9.8 * 2e2

But I'm not totally sure what all the symbols mean and how the answer was reached. Any help is appreciated!

Well, let's break it down and see if we can make it a bit more understandable, shall we?

First, let's take a look at the equation Total Energy (at end) = KE + PE. This equation states that the total energy at the end of the motion is equal to the sum of the kinetic energy (KE) and the potential energy (PE).

Now let's focus on the term Wdiss, which represents the work done by the non-conservative forces (friction and air resistance). We can calculate this by subtracting the kinetic energy (KE) and the potential energy (PE) from the work done on the car (Wdone). In other words:

Wdiss = Wdone - KE - PE

Now, let's plug in the given values. Wdone is given as 4.7e6 J (joules), which represents the work done on the car. KE can be calculated using the equation KE = (1/2)mv^2, where m is the mass of the car (1.5e3 kg) and v is the velocity (27 m/s). PE can be calculated as PE = mgh, where m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and h is the altitude above sea level (2e2 m).

So, simplifying the equation, we have:

Wdiss = 4.7e6 J - (0.5 * 1.5e3 kg * (27 m/s)^2) - (1.5e3 kg * 9.8 m/s^2 * 2e2 m)

You can plug in these values into a calculator or do the math step by step to find the value of Wdiss.

Let's break down the steps:

1. The question asks for the work done on the car by the combined forces of friction and air resistance, both of which are nonconservative forces. This work is referred to as "Wdiss".

2. To solve this problem, we need to find the values of Wdone (the work done on the car by the nonconservative force propelling it up the mountain road), KE (kinetic energy), and PE (potential energy).

3. Wdone is given in the problem as 4.70E6 J.

4. KE is the kinetic energy of the car, which is given by the formula KE = (1/2)mv^2, where m is the mass of the car (1.50E3 kg) and v is the speed of the car at an altitude of 2.00E2 m above sea level (27.0 m/s). Plugging in these values, we can calculate KE.

5. PE is the potential energy of the car, which is given by the formula PE = mgh, where m is the mass of the car (1.50E3 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the altitude of the car above sea level (2.00E2 m). Plugging in these values, we can calculate PE.

6. Now we can substitute the known values of Wdone, KE, and PE into the formula for Wdiss:

Wdiss = Wdone - KE - PE

Simply substitute the calculated values of KE and PE into the equation and solve for Wdiss:

Wdiss = 4.7E6 - 0.5 * 1.5E3 * (27.0)^2 - 1.5E3 * 9.8 * 2.00E2

Now you can evaluate this expression using a calculator to find the value of Wdiss.

Sure! Let's break down the symbols and equations used in solving this problem step by step:

1. First, we need to understand the given information:
- The car has a mass of 1.50E3 kg.
- The force doing work on the car is nonconservative and has done 4.70E6 J of work.
- The car starts from rest at sea level and has a speed of 27.0 m/s at an altitude of 2.00E2 m above sea level.

2. The problem asks us to find the work done on the car by the combined forces of friction and air resistance, which are both nonconservative forces. In order to find this, we need to calculate the work done by these forces and subtract it from the total work done on the car.

3. Next, we need to calculate the kinetic energy (KE) and the gravitational potential energy (PE) at the given altitude. The formulas for these energies are:
- KE = (1/2)mv², where m is the mass and v is the velocity (speed) of the car.
- PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height (altitude) above the reference level.

4. Since we need to subtract the work done by nonconservative forces from the total work done, we can express the work done by the nonconservative forces as Wdiss = Wdone - KE - PE, where Wdone is the total work done on the car. This formula accounts for the fact that the nonconservative forces have done work against the car's kinetic and potential energies.

5. Now we can substitute the given values and formulas into the equation:
- Wdiss = 4.7E6 J - (0.5 * 1.5E3 kg * (27.0 m/s)²) - (1.5E3 kg * 9.8 m/s² * 2.00E2 m)
= 4.7E6 J - 913.5E3 J - 2.94E6 J
= 4.7E6 J - 913.5E3 J - 2.94E6 J
= 2.85E6 J

Therefore, the work done on the car by the combined forces of friction and air resistance is 2.85E6 J.

I hope this explanation helps! Let me know if you have any further questions.