# Work-Kinetic Energy Theorem problem

• anne921
In summary, the problem involves a 2.1 X 10^3 kg car starting from rest at the top of a 20.0 degree sloped driveway, with an average friction force of 4.0 X 10^3 N opposing its motion. The car's speed at the bottom of the driveway is given as 3.8 m/s. To find the length of the driveway, the equation Wnet = Fd cos θ is used, where θ represents the angle between the net force and the displacement of the car. The angle of 20.0 degrees represents the energy gained from gravitational potential energy, while the angle θ' represents the angle at which the friction force acts. By calculating the
anne921

## Homework Statement

A 2.1 X 10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0 degrees with the horizontal. An average friction force of 4.0 X 10^3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?

## Homework Equations

Wnet - ΔKE = KEf - KEi
Wnet = Fd cos θ
Fnet = mgsinθ - Fk

## The Attempt at a Solution

I understand the basic idea of how to solve this problem. I think I would calculate Wnet using 1/2 mvf^2 (vi = 0); solve for Fnet and then substitute these values into solve for d by rearranging Wnet = Fdcosθ. My problem is that the key defines two angles - θ and θ'; with θ=20 degrees and θ' = 0. I don't understand where θ' comes into the picture. I am a Chemistry teacher trying to teach an intro physics course and I need some concrete help!

Presumably the θ' represents the angle that the friction force makes with the line of motion of the car (i.e., it acts parallel to the slope). Frictional forces always act to directly oppose the motion.

The other angle, θ, tells you the energy obtained from gravitational PE for a given distance traveled along the slope (since you can calculate the drop in height for the distance traveled).

It boils down to a conservation of energy problem; Energy gained through the drop in height in a gravitational field, energy lost to friction, remainder goes to KE of the car.

Thank you - that makes perfect sense. I didn't see that. I am finding that my biggest obstacle seems to be that I have difficulty seeing everything that is there. I appreciate your help!

## 1. What is the Work-Kinetic Energy Theorem?

The Work-Kinetic Energy Theorem is a fundamental principle in physics that states that the net work done on an object is equal to the change in its kinetic energy. In other words, the amount of work exerted on an object is directly proportional to the change in its speed or velocity.

## 2. How is the Work-Kinetic Energy Theorem used in problem solving?

The Work-Kinetic Energy Theorem is used to analyze the motion of objects and to calculate the amount of work required to change their speed. It is commonly used in problems involving forces, motion, and energy.

## 3. What are the units of work and kinetic energy?

The units of work are joules (J), while the units of kinetic energy are also joules (J). This is because work is defined as the product of force and displacement, while kinetic energy is defined as 1/2 times mass times velocity squared.

## 4. Can the Work-Kinetic Energy Theorem be applied to all types of motion?

Yes, the Work-Kinetic Energy Theorem can be applied to all types of motion, including linear, rotational, and oscillatory motion. It can also be used to analyze the work done by non-conservative forces, such as friction or air resistance.

## 5. Are there any limitations to the Work-Kinetic Energy Theorem?

While the Work-Kinetic Energy Theorem is a useful and widely applicable principle, it does have some limitations. It assumes that all forces are either conservative or non-conservative, and that no work is done by internal forces. It also does not take into account any changes in potential energy, only changes in kinetic energy.

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