# Which Force Application Minimizes Effort When Moving a Box?

• 21385
In summary, if you are pushing the box with a force downwards from the horizontal, you will be adding to the normal force, and thus the correct equation will be Ff=u(mg+FasinX).
21385

## Homework Statement

You want to apply a force on a box so that it moves with constant speed across a horizontal floor. The coefficient of kinetic friction between the box and the floor is u. Of the four following cases, the force you apply on the box will be smallest when you

a) Push on it with a force applied at an angle 0<X<90 downward from the horizontal;
b) pull on it with a force applied at the same angle X as in (a), upward from the horizontal;
c)do either (a) or (b) since the applied force is the same;
d)pull or push with a force applied horizontally

## Homework Equations

Ff=Fa, to keep at a constant speed

## The Attempt at a Solution

The correct answer is b but I have no idea why.
I chose c as my answer seeing that a and b would both result in the same thing, only that the weight of the box would concentrate in the front in situation (a) and that the weight would concentrate in the back in situation (b). I felt that this difference would not change the amount of force needed. Are there any other factors I have not considered? Thanks

The friction can be calculated by F=uR, where R is the normal reaction force. Do you know how to find the normal reaction force? More specifically, how will it be different when the force applied is a pull compared to when it is a push?

The friction equation is Ff=u(mg-FasinX).
I actually have no idea why the force would be different pushing from one side or pulling from the another.

21385 said:
The friction equation is Ff=u(mg-FasinX).
That's for a pull. If you are pushing the box with a force downwards from the horizontal, you will be adding to the normal force, and thus the correct equation will be Ff=u(mg+FasinX).

Cristo, interesting. You're adding ergonomics to the eqn. But i see the wisdom, at arms length to pull relieves N force while pushing adds to it.
Cheers.

thanks, cristo
omg, i am so stupid, i thought choice a) was pushing from the angle below the horizontal

Last edited:

## 1. What is the purpose of pushing and pulling boxes in a scientific context?

In scientific research, pushing and pulling boxes is often used as a way to study forces and motion. By manipulating the position and direction of the boxes, scientists can gather data and make observations about the effects of different forces on objects.

## 2. What are some real-world applications of studying pushing and pulling boxes?

Studying the physics of pushing and pulling boxes can have practical applications in fields such as engineering, transportation, and manufacturing. For example, understanding how different forces affect the movement of objects can help engineers design more efficient structures or vehicles.

## 3. How does friction play a role in pushing and pulling boxes?

Friction is a force that opposes the motion of objects. When pushing or pulling a box, friction between the box and the surface it is on can either help or hinder the movement. The type of surface and the weight of the box can also affect the amount of friction present.

## 4. Is there a difference between pushing and pulling boxes in terms of the forces involved?

Yes, there is a difference between pushing and pulling boxes. When pushing a box, the force is applied in the same direction as the movement of the box. When pulling a box, the force is applied in the opposite direction of the movement.

## 5. How can the study of pushing and pulling boxes contribute to our understanding of Newton's Laws of Motion?

Newton's Laws of Motion describe how objects move in relation to the forces applied to them. By studying pushing and pulling boxes, scientists can observe and gather data on how forces affect the motion of objects, providing evidence for these laws and helping us better understand the principles of motion.

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