Solving a Crate Motion Problem: Find Time for 4m Movement

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SUMMARY

The discussion focuses on solving a physics problem involving the motion of a crate pushed by a force of 400N at a 35.2-degree angle. The crate's weight is 300N, and the coefficient of kinetic friction is 0.57. The user calculated the net forces and acceleration, concluding that the time taken to move the crate 4 meters from rest is approximately 1.57 seconds. However, the user expressed uncertainty about the frictional force calculation, specifically the value of 171.1N, indicating a potential error in their approach to determining the normal force.

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  • Understanding of Newton's laws of motion
  • Familiarity with frictional force calculations
  • Knowledge of vector components in physics
  • Ability to solve quadratic equations for motion
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  • Study the derivation and application of the frictional force formula Fk = μFn
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Homework Statement



A woman pushes a crate with a force of 400N downward at a 35.2 angle down below horizontel. The crate weighs 300N. If coeffiecient of kenetic friction is 0.57, how much time does it take to move box 4m from rest.

Homework Equations



Fg=mg
Fk=(muk)mg

The Attempt at a Solution



I found fg by multiplying mass and gravity, I got 300N. Next I found Fk by multiplying micro by mass and gravity and got 171.1N.

Found gravity by doing 300/9.81 and got 30.6Kg.

Did

Fnety=Fn+Fay-Fg=0
0=Fn+400sin35.2-300
0=Fn+230.6-300
Fn=69.4

Fnetx=Fax-Fk
ma=Facostheta-Fk
30.6a=400cos35.2-171.1
30.6a=326.9-171.1
30.6a=155.9
a=5.1m/s2

Next i used d=V1t+.5at2
4=0t+.5(5.1)t2
4=2.55t2
t=1.57s

But I do not think I got the correct answer because I did not use the t2 after the 2.55 in anyway to find the answer. Did I do the rest of the work correct and just did the calculating of the time wrong, or is my other work wrong?

thanks!
 
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I think the problem is with this part:

Fnetx=Fax-Fk
ma=Facostheta-Fk
30.6a=400cos35.2-171.1
30.6a=326.9-171.1
30.6a=155.9
a=5.1m/s2

Where does 171.1N come from? Normally frictional force is \mu F_N.
 
Dont think so because I used the Fk= formula, and in the process I was trying to find Fn and I didnt know it so I used a different formula.

Fk=Ff

And Fk= muk x m x g

Fk= 0.57(30.6)(9.81)

I think it is in the ending but not sure, I just know the answer is wrong.