Demode cant simplify equations =(

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The discussion revolves around calculating the minimum force required to drag a 40 kg carton of books across the floor at a 45-degree angle, with a coefficient of friction of 0.60. The user initially struggles to solve the equations derived from the free body diagram but eventually arrives at a force of 207.41 N after further consideration. Key to solving the problem is expressing the normal force from one equation and substituting it into the other to find the minimum force. The user acknowledges their oversight and expresses gratitude for the assistance received. The final answer confirms the calculations and understanding of the physics involved.
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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:
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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!
 

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