# Conservation of energy and fricion

• haha01hah
In summary, the conversation is about a homework assignment to calculate the distance a car will travel before coming to a stop on a steep road. The car starts with a speed of 2m/s on a 35 degree inclined road and then travels on a straight road with a friction constant of 0.08. The height difference between the top of the hill and the straight road is 133 meters. The conversation also includes a question about whether the initial potential energy term can be omitted in the calculation. The solution is that since the initial point is already at the top of the hill, the potential energy term can be canceled out.
haha01hah

## Homework Statement

Got an assignment from the teacher to present a problem I have made by myself and show how I have done it, so I have no answer to refer to in this particular question. Anyways,

A car is pushed so that it gains a speed of 2m/s just off a steep road, which has an angle of 35 degrees from the ground. Assume the friction constant is 0.07 from the top to the bottom of the hill. After the steep road, the road is straight. Between the tires and the ground on this straight road the friction is 0.08. The difference in height is 133 meters (from the straight ground to the top of the hill). Assume no force other than the friction that is working against the motion. I want to calculate the distance before it stops.

So I have calculated the speed at the bottom, which is 49,3 m/s. But, to calculate the distance the car needs to stop I use;

$$1/2mv^2+mhg=1/2mv_0^2+mgh_0+W_R$$

Ok, now to my question;
I know that I should cancel out the first two terms (1/2 mv^2 + mgh), but am I allowed to calcel out $$mgh_0$$ because I don't anymore do use the height difference, given that I already calculated the speed at the beginning of the straight road?

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## The Attempt at a Solution

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Last edited:
Sure. If you started at the top of the hill as your initial point, and used the end of the motion as your final point, then you'd have to include the initial PE. But since you did it the other way, you can omit the PE terms on both sides.

## 1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

## 2. How does friction affect energy conservation?

Friction is a force that opposes motion between two surfaces in contact. When an object experiences friction, some of its kinetic energy is converted into heat energy, resulting in a decrease in the total amount of energy in the system.

## 3. What is the role of friction in energy conservation?

Friction plays a crucial role in energy conservation by converting some of the kinetic energy of moving objects into heat energy. This helps to slow down the object and prevent it from gaining too much momentum, thus conserving energy in the system.

## 4. How can we reduce the effects of friction on energy conservation?

One way to reduce the effects of friction on energy conservation is by using lubricants or smoother surfaces to reduce the amount of contact between moving objects. Another way is to design systems with lower frictional forces, such as using ball bearings or air cushions.

## 5. What are some real-world applications of energy conservation and friction?

Energy conservation and friction have many real-world applications, such as in the design of efficient machines and engines. Friction is also important in everyday activities like driving a car or riding a bike, where it helps to slow down and control the motion of the vehicle.

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