Wrong answer for torque question but why?

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In summary: Additionally, you did not use the fact that the plank remains in equilibrium for any value of θ less than 70 degrees. In summary, you have not correctly calculated the coefficient of static friction between the plank and the ground.
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auk411
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Homework Statement



A a uniform plank of L = 6.10 m and weight 445 N, rests on the ground and on a frictionless roller at the top of a wall of height 3.05 m. The plank remains in equilibrium for any value of theta less than 70 degrees, but slips if theta bigger or equal to 70 degrees. What is the coefficient of static friction between the ladder and the ground?

Homework Equations



N_2 = normal force between plank and ground. N_1 equals the normal force of the roller onto the plank.
F with no subscripts = fs, aka. the friction force (which is pointing to the right)
[tex]\mu[/tex]s=Fs/N2

The Attempt at a Solution



F_net(x) = F - N1[tex]\theta[/tex]
Fnet(y) = N2+1cos[tex]\theta[/tex] -W (the weight) =0
T(Torque)taken about the middle = Fsh - N2htan[tex]\theta[/tex]=0

N1=F/tan[tex]\theta[/tex]

N2 + F/(sin[tex]\theta[/tex]cos[tex]\theta[/tex]) =W [comes from Fnet(y) with F/sin[tex]\theta[/tex] being plugged in for N1.

W = N2 + Fcot[tex]\theta[/tex]

W = F/tan[tex]\theta[/tex] + Fcot[tex]\theta[/tex] (plugging in N2 = F/tan[tex]\theta[/tex])

W = F ( 1/tan[tex]\theta[/tex] + cot ([tex]\theta[/tex])

...It keeps going on until you reach that the coefficient of friction equals tan[tex]\theta[/tex], which is the wrong answer
 
Last edited:
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  • #2
. Where did I go wrong?You didn't calculate the force of friction correctly. The force of friction should be F=μN2, where μ is the coefficient of friction. You calculated it as F=Fsh-N2htanθ, which is not correct.
 

1. What is torque and why is it important?

Torque is a measure of the twisting force applied to an object. It is important because it determines the rotational motion of an object and is a key concept in understanding how machines and engines work.

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Torque is calculated by multiplying the force applied to an object by the distance from the point of rotation to the point where the force is applied. The unit of torque is Newton-meters (Nm) in the metric system.

3. What happens if the wrong answer is given for a torque question?

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5. How can one improve their understanding of torque?

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