# How Do Two Applied Forces and Kinetic Friction Affect Crate Acceleration?

• jarmen
In summary, a 28.8-kg crate is initially at rest and is being acted upon by two forces, F1 and F2, in a downward direction. The coefficient of kinetic friction between the crate and the floor is k = 0.374. By finding the net applied force and considering the y-axis, the magnitude and direction of the total applied force can be determined, which will also be the direction of the acceleration. To find the magnitude of the acceleration, the friction force, which opposes motion, must also be taken into account.
jarmen
The drawing shows a 28.8-kg crate that is initially at rest. Note that the view is one looking down on the top of the crate. Two forces, F1 and F2, are applied to the crate, and it begins to move. The coefficient of kinetic friction between the crate and the floor is k = 0.374. Determine the (a) magnitude and (b) direction (relative to the x axis) of the acceleration of the crate.

## Homework Statement

m=28.8kg
k(kinetic friction)=.374
F1=88N
F2=54N

## Homework Equations

fk(magnitude of kinetic friction)= (k)(Fn)
ax= (-fk)/m

## The Attempt at a Solution

I have tried a few things, but i am not sure really what equation to go after, since i feel i should be using something with the angles in it.

any help is appreciated.

#### Attachments

• ch04p_45.gif
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Start by finding the net applied force. Add up the F1 and F2 force vectors. Don't forget that they are vectors, not just numbers.

so for getting the magnitude to the right, along the x-axis shouldn't i do
cos(55) (88) =50.47

104.47

If this is right, then where do i go from here.

That's the sum of the vectors on the x-axis. To complete the vector addition you need to consider y-axis too.

would that be (sin(55))(88) for Y vector?

jarmen said:
would that be (sin(55))(88) for Y vector?
That's correct. That's the y-component of the applied force.

Use the components that you've calculated for the total applied force to find the magnitude and direction of the total applied force. The direction of the applied force will also be the direction of the acceleration.

To find the magnitude of the acceleration you will have to include friction, which opposes the motion and acts opposite to the applied force. What's the friction force? What's the total force (not just the applied force) acting on the box?

Ok i got it,
thanks everyone i just worked it out and it was correct.

## 1. What is the definition of kinetic friction?

Kinetic friction is the force that opposes the relative motion between two surfaces in contact when there is movement or sliding between them.

## 2. How is the magnitude of kinetic friction determined?

The magnitude of kinetic friction is determined by the coefficient of kinetic friction, which is a dimensionless constant that depends on the nature of the surfaces in contact and the normal force acting between them.

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

The magnitude of kinetic friction is affected by the nature of the surfaces in contact, the normal force, and the relative velocity between the two surfaces.

## 4. Can kinetic friction be greater than static friction?

In most cases, kinetic friction is lower than static friction. However, there are some cases where the coefficient of kinetic friction is higher than the coefficient of static friction, resulting in a greater magnitude of kinetic friction.

## 5. How does the direction of kinetic frictional force compare to the direction of motion?

The direction of kinetic frictional force is always opposite to the direction of motion. This means that if an object is moving in one direction, the kinetic frictional force will act in the opposite direction.

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