# Kinetic Friction ProblemNeed Help

• mixedtape_15
In summary, the box is being pulled along a horizontal surface by means of a rope, and the coefficient of kinetic friction between the box and the surface is 0.330. When working out the acceleration of the box, you use the normal force and weight and cosine of the angle in the y direction, and the kinetic friction (normal force times kinetic friction coefficient) and weight and sine of the angle in the X direction. You then solve it all and get -1.59 m/s^2. However, the box isn't going anywhere because there is no acceleration in the y direction.
mixedtape_15
Kinetic Friction Problem..Need Help!

Okay...so I really think I'm doing this right..but the CAPA thing won't take my answer so there has to be something I'm doing wrong.
The Question is ...
A 32.0 kg box is being pulled along a horizontal surface by means of a rope that exerts a force of 265 N at an angle of 54.5o above the horizontal. The coefficient of kinetic friction between the box and the surface is 0.330. What is the acceleration of the box?

So I drew my free body diagram and I had the Normal Force and the Weight and cosine of the angle in the y direction and I had the kinetic friction (normal force times kinetic friction coefficient) and weight and sine of the angle in the X direction.

Then I worked it all out and I got
Fy = may
Fy = 0
N - W(cos54.5) = 0
N - mg(cos54.5) = 0
N = 32.0kg (9.81 m/s^2)(cos54.5)
N = 182.3

Fx = max
-fk + T - w(sin54.5) = max
T - (N x uk) - mg(sin54.5) = max
265 - (182.3 x 0.330) - (32kg)(9.81m/s^2)(sin54.5) = 32kg(ax)
then I solved It all and it worked out to be -1.59 m/s^2
but its saying its not right..so I'm confused beyond belief now.

Check your trig functions in calculating N.

I've switched the trig functions around and tried that answer but still nothing. and I'm almost positive I have my trig done right anyways...but thanks.

mixedtape_15 said:
I've tried this already but it didn't help..besides I'm almost positive that I have my trig done right.

So you're sure $$N - w \cos{54.5} = 0$$?

well there is no acceleration in the y direction so I guess it would have to be that.

Look at the x- and y-components of all the forces, and determine what you have.

$$\Sigma F_{x} = T_{x} - F_{f}$$

$$\Sigma F_{y} = N + T_{y} - mg$$

mixedtape_15 said:
well there is no acceleration in the y direction so I guess it would have to be that.

Why the cosine? Like I said, rethink your trig.

I didn't think you had to incorporate the tension into the Y direction...isn't it just in the X?

mixedtape_15 said:
I didn't think you had to incorporate the tension into the Y direction...isn't it just in the X?
Re-read the question, and redraw your free body diagram. The surface is horizontal, but the rope is not.

There is certainly a y-component of the tension, and it alleviates some of the normal force.

okay I'll go do that and hopefully figure this out..thanks

Okay I just redid it and realized my stupid mistake. I thought that the box was on a slope..but then when I reread it I realized that the box was on a straight horizontal and it was the rope that was on the angle. Thanks a bunch! :D

## What is kinetic friction?

Kinetic friction is the force that resists the movement of an object when it is in contact with another surface. It is also known as sliding friction and is caused by the microscopic irregularities of the two surfaces rubbing against each other.

## How is kinetic friction different from static friction?

Kinetic friction occurs when an object is already in motion, while static friction occurs when an object is at rest. Static friction is typically greater than kinetic friction, as it takes more force to overcome the initial resistance of an object at rest.

## What factors affect the magnitude of kinetic friction?

The magnitude of kinetic friction is affected by the nature of the two surfaces in contact, the force pressing the surfaces together, and the speed at which the object is moving. Friction also increases with rougher surfaces and larger masses.

## How is kinetic friction calculated?

Kinetic friction can be calculated using the formula Fk = μkN, where Fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force exerted by the surfaces on each other.

## What are some real-life examples of kinetic friction?

Kinetic friction can be observed in many everyday activities, such as walking on a sidewalk, braking a car, or rubbing hands together to create warmth. It is also important in industrial processes, such as the movement of machinery and the production of heat through friction.

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