# Calculating Work and Friction on a Crate on an Incline

• Sheneron
In summary, the problem involves a crate of mass 10.6 kg being pulled up a rough incline with an initial speed of 1.48 m/s. The pulling force is 104 N at an angle of 20.1° with the horizontal and the crate is pulled a distance of 5.05 m. Part A asks for the work done by the gravitational force, which was calculated to be -180 J. Part B asks for the increase in internal energy of the crate-incline system due to friction. This can be found by calculating the work done by friction, which rubs the molecules beneath the crate and heats it up, resulting in an increase in internal energy.

## Homework Statement

A crate of mass 10.6 kg is pulled up a rough incline with an initial speed of 1.48 m/s. The pulling force is 104 N parallel to the incline, which makes an angle of 20.1° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.05 m.

(a) How much work is done by the gravitational force on the crate?
(b) Determine the increase in internal energy of the crate-incline system due friction.

## The Attempt at a Solution

I have solved part A, and I got -180 J. I need help on B. I really don't know what the question is looking for. Thanks

Increase in internal energy is decrease in kinetic energy.

It may be easier to think about it in terms of the definition of work done by a force. That is,

$$W = \int Fds$$

where the work done by friction rubs the molecules beneath the crate and heats it up, hence an increase in internal energy.

So do I need to find the Work that is done by friction?

## 1. How do you calculate the work done on a crate on an incline?

To calculate the work done on a crate on an incline, you will need to use the formula W = Fd cosθ, where W is the work, F is the force applied, d is the displacement of the crate, and θ is the angle of the incline. You will also need to account for the weight of the crate and the force of friction.

## 2. What is the formula for calculating friction on a crate on an incline?

The formula for calculating friction on a crate on an incline is Ff = μFn, where Ff is the force of friction, μ is the coefficient of friction, and Fn is the normal force. The normal force can be calculated by multiplying the mass of the crate by the acceleration due to gravity.

## 3. How does the angle of the incline affect the work and friction on a crate?

The angle of the incline affects the work and friction on a crate by changing the value of the cosine in the work formula and the normal force in the friction formula. As the angle increases, the work and friction will also increase, and vice versa.

## 4. Is the work done on a crate on an incline always positive?

No, the work done on a crate on an incline can be positive, negative, or zero. It depends on the direction of the force and the displacement of the crate. If the force and displacement are in the same direction, the work will be positive. If they are in opposite directions, the work will be negative. If there is no displacement, the work will be zero.

## 5. How can friction be reduced on a crate on an incline?

To reduce friction on a crate on an incline, you can decrease the coefficient of friction by using a smoother surface or adding lubrication. You can also reduce the weight of the crate or decrease the angle of the incline. Additionally, using wheels or rollers can help reduce friction on the crate.