# Demode cant simplify equations =(

• demode
In summary, 207.41 N is the minimal force needed to drag a carton of books across the floor if the force is applied at an angle of 45 degrees to the horizontal.
demode
I was given the problem: "What minimum force is required to drag a carton of books across the floor if the force is applied at an angle of 45 degrees to the horizontal? Take the mass of the carton as 40 kg and the coefficient of friction as 0.60.

Free Body Diagram (Given by physics teacher)
http://img327.imageshack.us/img327/4383/untitled1yz4.th.jpg

Equations
$$F\sin(45) + F_n = mg$$
$$\mu_k F_n = F\cos(45)$$

Now for the life of me, I can't seem how to solve for F since the question asks for the minimum force.. Will i just need to solve the system of equations that I have?**EDIT**
After some simple math and slapping myself repeatedly for being so blind, i came up with 207.41 as the force.. Would anyone be willing to confirm that answer with me?

Last edited by a moderator:
Hint

cos 45 and sin 45 are the same.

If you equate these two now you have just Fn as the unknown - find it and substitute it back to find F*

Minimum force just means no acceleration ie exactly balanced forces.

demode said:
I was given the problem: "What minimum force is required to drag a carton of books across the floor if the force is applied at an angle of 45 degrees to the horizontal? Take the mass of the carton as 40 kg and the coefficient of friction as 0.60.

Free Body Diagram (Given by physics teacher)
http://img327.imageshack.us/img327/4383/untitled1yz4.th.jpg

Equations
$$F\sin(45) + F_n = mg$$
$$\mu_k F_n = F\cos(45)$$

Now for the life of me, I can't seem how to solve for F since the question asks for the minimum force.. Will i just need to solve the system of equations that I have?

**EDIT**
After some simple math and slapping myself repeatedly for being so blind, i came up with 207.41 as the force.. Would anyone be willing to confirm that answer with me?

Express the normal force Fn out of the first equation, and plug it into the second equation. Then solve for F, and you'll get the minimal force.

Last edited by a moderator:
Alright guys thanks so much.. Perhaps I should have thought harder before turning to the forums for help.. Once again thanks!

## 1. Why is it important to simplify equations?

Simplifying equations helps make them easier to understand and work with. It also allows us to identify key patterns and relationships within the equation.

## 2. What are the common methods for simplifying equations?

The most common methods for simplifying equations include combining like terms, factoring, and using the distributive property.

## 3. How do I know when an equation is already simplified?

An equation is considered simplified when all like terms have been combined and there are no more common factors that can be factored out.

## 4. Can simplifying an equation change its solution?

No, simplifying an equation does not change its solution. It only makes the equation easier to work with and understand.

## 5. Are there any shortcuts or tips for simplifying equations?

Yes, some common shortcuts for simplifying equations include using the exponent rules, multiplying by the reciprocal, and using the quadratic formula.

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