What Is the Maximum Angle Theta for Equilibrium in a Statics Weight Problem?

[ninjagowoowoo]

One end of a uniform meter stick is placed against a vertical wall. The other end is held by a lightweight cord that makes an angle theta with the stick. The coefficient of static friction between the end of the meter stick and the wall is 0.370 .

What is the maximum value the angle theta can have if the stick is to remain in equilibrium?

Maybe someone could point me in the right direction. so far I've calculated the sum of torques (equal to zero for equilibrium) and i got xf=(1-x)Tsin(theta)
where f is friction and T is the tension in the cord. Also i know that f=(0.37)N. I have no idea what else I can use here. Please help! Thanks.

 

[Nylex]

The sum of the forces is also zero for equilibrium. Have you drawn a diagram? Those help lots for questions like this. Also, you said "Also i know that f=(0.37)N". This is not true, the coefficient of friction, \mu is 0.37. The frictional force itself is F = \muR, where R is the normal reaction.

 

[thepatientmental]

To solve this problem, we can use the equation for static friction: f = μN, where μ is the coefficient of static friction and N is the normal force. In this case, the normal force is equal to the weight of the meter stick, which we can calculate using the formula W = mg, where m is the mass of the meter stick and g is the acceleration due to gravity (9.8 m/s^2).

Next, we can use trigonometry to relate the angle theta to the length of the meter stick and the distance from the wall. This will give us the value of N, which we can plug into the equation for static friction.

Finally, we can set the sum of torques equal to zero and solve for theta. This will give us the maximum angle theta can have for the stick to remain in equilibrium.

I hope this helps guide you in the right direction. It's important to remember to always consider all the forces acting on the object and use the appropriate equations to solve for the unknown variables. Good luck!