(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

To move a large crate across a rough floor, you push on it with a force F at an angle of 21° below the horizontal, as shown in the figure. Find the force necessary to start the crate moving, given that the mass of the crate is m = 37 kg and the coefficient of static friction between the crate and the floor is 0.60.

2. Relevant equations

[tex]F_x=F\cos{\theta}[/tex]

[tex]F_y=F\sin{\theta}[/tex]

[tex]F=ma[/tex]

[tex]W=mg[/tex]

[tex]f_s=\mu_sN[/tex]

3. The attempt at a solution

so i know that [tex]\sum{\vec{F_x}}=F\cos{\theta}-\mu_sN=0[/tex]

and [tex]\sum{\vec{F_y}}=N-F\sin{\theta}-mg=0[/tex]

solving for [itex]N[/itex] i get [itex]N=F\sin{\theta}+mg[/itex] and plugging this in for N in the sum of the forces in the x direction i get [itex]F\cos{\theta}-\mu_s(F\sin{\theta}+mg)=0[/itex] and finally solving for [itex]F[/itex] i get [itex]F=\frac{\mu_smg}{\cos{\theta}-\mu_s\sin{\theta}}[/itex]

so i plugged in all the values given and yet i still got the wrong answer (my homework is online and i get 5 tries for each question)

my guess is that im using the wrong angle, should it be 21? or 360-21=339?

or did i not solve for [itex]F[/itex] correctly?

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# Homework Help: Force with static friction

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