# Statics Friction problem -- A 500lb box is being pushed up a ramp

• nmelott
In summary, the conversation discusses a problem involving a 500lb box being pushed up a ramp with a slope of 10 degrees. The center of mass of the box is at the geometric center of the area and the question asks for the force P that will cause the box to tip and slide, given coefficients of friction and the weight of the box. The solution involves using a moment equation to solve for the force that causes the box to tip, and using the sum of forces in the x direction to solve for the force that causes the box to slide. It is noted that the box will slip before it will tip if the static friction does not provide enough counter force.
nmelott

## Homework Statement

A 500lb box is being pushed up a ramp which is sloped at 10 deg. The center of mass of the box is at the geometric center of the shown area. If the static coefficient of friction is 0.35 and the kinetic coefficient of friction is 0.28, what is the force P that will cause the box to tip? What is the force P that will cause the box to slide?

## Homework Equations

*I resolved the weight into x and y components as my online homework allows me to set the axis to whatever I want, so I set it to move 10 degrees.
Wx=Weight*sin(10)
Wy=Weight*cos(10)[/B]
ΣFx:0=P-Slipping Force-Wx
ΣFy:0=N-Wy
Slipping force= μ(kinetic)N
θ

## The Attempt at a Solution

So I solved for the force P that causes the box to slide by the sum of the forces in the x direction.
P=Slipping Force+Wx
P=μ(kinetic)N+Weight*sin(10)
P=.28*Weight*cos(10)+Weight*sin(10)
P=.28*500*cos(10)+(500*sin(10))=224.7lb

That is correct, but I keep getting the wrong answer for the force that causes the box to tip. I am using a moment equation about the right bottom corner of the box(it is being pushed from the left, top side) and setting it equal to zero. Is a moment equation the right way to go about this or am I using the wrong approach?

A moment equation about the point where the box will tip is the correct approach. How far off the center of mass does the force P push?

Note that it would be impossible to tip the box if the static friction doesn't give enough counter force. So in other words the box would slip before it would tip.

P is pushing 15in above the center of the box. The box's dimensions (probably should've included) are
Height=70in
width=30in
The distance from the bottom to force P is 50 in

## 1. What is static friction and how does it relate to the problem?

Static friction is a type of force that acts between two surfaces that are in contact with each other but not moving relative to one another. In this problem, the static friction force is what prevents the 500lb box from sliding down the ramp.

## 2. How do you calculate the static friction force in this problem?

The static friction force can be calculated using the formula F = μsN, where F is the friction force, μs is the coefficient of static friction, and N is the normal force exerted by the ramp on the box. The coefficient of static friction is a constant that depends on the materials of the two surfaces in contact.

## 3. What factors affect the static friction force in this problem?

The static friction force depends on the coefficient of static friction, which is determined by the materials of the surfaces in contact. It also depends on the normal force exerted by the ramp on the box, which is affected by the angle of the ramp and the weight of the box.

## 4. How does the angle of the ramp affect the static friction force?

The angle of the ramp affects the normal force exerted by the ramp on the box, which in turn affects the static friction force. As the angle increases, the normal force decreases, which means the static friction force needed to keep the box from sliding down the ramp also decreases.

## 5. What is the maximum angle at which the box can be pushed up the ramp without sliding?

The maximum angle at which the box can be pushed up the ramp without sliding is determined by the coefficient of static friction. The angle is equal to the inverse tangent of μs, so as long as the angle of the ramp is less than this value, the box will not slide. Beyond this angle, the static friction force will no longer be strong enough to prevent the box from sliding down the ramp.

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