# Constant velocity and the coefficient of kinetic friction

• kinthos
In summary, the coefficient of kinetic friction between the tires of the wagon and the pavement is 0.781.
kinthos
"A child rides a wagon down a street with an inclination angle of 38.0 degrees. In order to keep from moving to fast, the child has secured the wheels of the wagon so that they do not turn. The wagon and the child then slide down the hill at constant velocity. What is the coefficient of kinetic friction between the tires of the wagon and the pavement?"

I've thought about this for awhile. I had thought that the coefficient of kinetic friction would equal the coefficient of static friction (because the net force at constant velocity and at rest equals 0), but now I'm not sure. I'm fairly certain that the coefficient of kinetic friction can't equal 0 (there would be no friction at all then), but beyond that I'm not sure. Any ideas?

What forces act on the "child + wagon"? Since it moves at constant velocity, what must the net force be in any direction?

Well, the force of kinetic friction and the force that causes the motion would sum to 0 N (the two forces would be equal in magnitude but opposite in direction). The only forces that act on the child and the wagon would be the weight, friction, and applied force...unless you include the normal force, which is the component of the weight perpendicular to the incline. What I don't understand, though, is how to find the coefficient of kinetic friction without a given mass or applied force.

There's no applied force--the kid's just sliding down the incline. (Nobody is pushing or pulling, just gravity.) Now analyze the forces acting parallel to the incline.

Mmm...uk (coefficient of kinetic friction) = friction/normal force. Friction = weight(sin 38) and normal force = weight(cos 38). Reducing this fraction to lowest terms would produce sin/cos, which = tan...uk = tan 38 = 0.781. Would this be correct?

Good job! Looks good.

## 1. What is constant velocity?

Constant velocity refers to an object moving at a steady speed in a straight line with no change in direction. It is often represented by the symbol "v" and is measured in units of distance per time (such as meters per second).

## 2. How is constant velocity related to the coefficient of kinetic friction?

The coefficient of kinetic friction is a measure of the amount of friction between two surfaces in motion. When an object is moving at a constant velocity, the forces acting on it must be balanced, meaning that the force of friction is equal to the force pushing or pulling the object. The coefficient of kinetic friction is used to calculate this force of friction.

## 3. What factors affect the coefficient of kinetic friction?

The coefficient of kinetic friction is affected by the roughness of the two surfaces in contact, the weight of the object, and the materials of the surfaces. The rougher the surfaces, the higher the coefficient of kinetic friction will be. A heavier object will also have a higher coefficient of kinetic friction, while different materials can have varying coefficients of kinetic friction.

## 4. How is the coefficient of kinetic friction measured?

The coefficient of kinetic friction is typically measured using an apparatus called a friction tester. This device measures the force required to keep an object moving at a constant velocity across a surface. The ratio of this force to the weight of the object is the coefficient of kinetic friction.

## 5. What is the significance of the coefficient of kinetic friction?

The coefficient of kinetic friction is an important factor in understanding and predicting the motion of objects. It helps engineers and scientists design and build machines and structures, as well as predict how objects will move in different situations. It is also used in everyday life, such as in the design of car tires and the creation of non-slip surfaces.

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