# Frictional forces and the angle for minimum frictional force

• Yam
In summary: Or is there a vertical force involved that makes the box hover ?In summary, the problem involves a person dragging a packing crate across a rough floor and trying to find the minimum angle for the pulling force to keep the crate moving at a constant velocity. The equation for frictional force is given as Uk(mg)(cosx), but additional equations are needed to solve the problem. The forces that play a role include the pulling force, frictional force, and weight of the crate. The magnitude of the pulling force may depend on the angle, and there may be a minimum force required to keep the crate moving.
Yam

## Homework Statement

A person is dragging a packing crate of mass 100 kg across a rough floor where the coefficient of kinetic friction is 0.400. He exerts a force F just sufficient to keep the crate moving at a constant velocity. At what angle above the horizontal should his pulling force F be for it to be minimum?

## Homework Equations

Frictional Forces = UkN

## The Attempt at a Solution

Frictional Force = Uk(mg)(cosx)

Im stuck.

I like the "I'm stuck" (you wouldn't post if you weren't). But ##F_{fric} = \mu_k mg\cos\theta## doesn't count as an attempt.

What forces play a role and how can you express the constant speed in an equation ?

Forces that play a role:
1) Pulling force F
2) Frictional force

Constant speed means that there is no acceleration.
F = ma = m(0) = 0

Frictional force is horizontal, pulling is in some theta direction. What else ? (hint: you already wrote mg -- and there's no vertical acceleration either). So we have a few equations. Magnitude of pulling force might depend on theta. If so, there might be a minimum !

Forces that play a role:
1) Pulling force F at an angle
2) Horizontal Frictional force
3) Weight of the block

Yes i understand that the magnitude of the puling force depends on theta, however, how do i relate it to the minimum force?

One force missing still.
If |F| depends on theta like, say ##2-\cos^2\theta## then zero degrees would give a nice minimum, wouldn't it ?

Is it the upward force generated by the pull at an angle?

Wouldn't that mean that if you don't pull, the box drops down like a brick ?

## 1. What are frictional forces and why are they important?

Frictional forces are the resistance that occurs when two surfaces are in contact and trying to move past each other. They are important because they can affect the motion and stability of objects, as well as the amount of energy required for movement.

## 2. How is the angle for minimum frictional force determined?

The angle for minimum frictional force is determined by finding the angle at which the normal force and the force of friction are equal in magnitude. This is known as the angle of repose and can be calculated using trigonometry.

## 3. What factors affect the amount of frictional force?

The amount of frictional force depends on the types of materials in contact, the surface roughness, and the amount of force applied. Other factors such as temperature and lubrication can also affect the amount of frictional force.

## 4. How can the angle for minimum frictional force be minimized?

The angle for minimum frictional force can be minimized by using materials with smoother surfaces, reducing the amount of force applied, or using lubricants to reduce the friction between surfaces. Additionally, changing the angle of contact between the surfaces can also affect the amount of frictional force.

## 5. What are some real-life applications of understanding frictional forces and the angle for minimum frictional force?

Understanding frictional forces and the angle for minimum frictional force can be useful in various real-life situations, such as designing efficient machinery, improving the performance of vehicles, and preventing accidents caused by slippery surfaces. It can also be applied in sports, such as determining the optimal angle for a ski slope to reduce friction and increase speed.

• Introductory Physics Homework Help
Replies
4
Views
860
• Introductory Physics Homework Help
Replies
6
Views
982
• Introductory Physics Homework Help
Replies
13
Views
928
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
8K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
421
• Introductory Physics Homework Help
Replies
4
Views
3K