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

AI Thread Summary
A woman pushes a crate weighing 300N with a force of 400N at a 35.2-degree angle, and the coefficient of kinetic friction is 0.57. The calculations for gravitational force and normal force were performed correctly, but there is confusion regarding the frictional force, which should be calculated using the formula Fk = μFn. The net force in the x-direction was calculated as 155.9N, leading to an acceleration of 5.1 m/s². However, the final time calculation for moving the crate 4m appears to be incorrect, as the frictional force was not accurately derived. The user is uncertain if the earlier calculations were correct or if the time calculation is where the error lies.
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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.
 

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