Solve Torque Beam Problem: Mass Calculation

[Julian3]

Homework Statement

The beam is 47 cm in length. The other length measurements are R1 = 11 cm, and r2 = 26cm. The mass of the beam is 6.0 kg. Determine the mass on the beam.

Homework Equations

τ= F(R)Sinδ ( don't know if the circle thing is theta closest one i could find for it.

The Attempt at a Solution

Well I wrote out a net torgue equation ξτ=τ(triangle) - τ(rectangle) and then i got to the torque of the rectangle would be MG sin δ but and then re arranged to fine M but I don't know how to get the τ(Triangle) because it dosent give us the force to solve for it and I am kinda lost; i also said the radius was 10cm.

<Mentor note: duplicate images removed>

 

[Julian3]

didnt mean to upload same picture three times and don't know why its upside down

 

[gneill]

If the system is in balance then all the individual forces will be vertical, perpendicular to the beam. So you shouldn't need any trig functions for this problem.

Label your diagram with the individual forces acting on the beam. Hint: The beam itself can be divided into separate mass sections on either side of the fulcrum.

 

[Julian3]

If the system is in balance then all the individual forces will be vertical, perpendicular to the beam. So you shouldn't need any trig functions for this problem.

Label your diagram with the individual forces acting on the beam. Hint: The beam itself can be divided into separate mass sections on either side of the fulcrum.

And the fulcrum is the triangle right?

 

[gneill]

And the fulcrum is the triangle right?

Right.

 

[Julian3]

Okay so we have the MG from the rectangle and we have Fa from the fulcrum and the length is 20 cm but the radius from the rectangle is 11 cm and I know you have to solve for mass but I still don't get how to get the force from the fulcrum?

 

[gneill]

Okay so we have the MG from the rectangle and we have Fa from the fulcrum and the length is 20 cm but the radius from the rectangle is 11 cm and I know you have to solve for mass but I still don't get how to get the force from the fulcrum?

You can choose any location as a center of rotation about which to find the torques. An end of the beam may not be the best choice in this case. You want the system to balance about the fulcrum, so wouldn't that make a better choice for the center of rotation?

 

[Julian3]

You can choose any location as a center of rotation about which to find the toques. An end of the beam may not be the best choice in this case. You want the system to balance about the fulcrum, so wouldn't that make a better choice for the center of rotation?

Im sorry i get what your trying to say but i just can't relate that to help me because in my mind this is how I am working it out Στ=τ(folcum) + -τ(rectangle) and the rectangle is mg and i know the net force is 0 but i don't get what you are trying to say ? I am sorry for being so helpless i just don't understand this at all

 

[gneill]

There are three masses to be concerned about here. The beam is comprised of two masses, one on each side of the fulcrum. The rectangle is the third mass. Each mass presents a force due to its weight. Each force is on one side of the fulcrum or the other. So each causes a torque about the fulcrum.

Can you identify the locations where each of the masses applies its force with respect to the fulcrum? What are their distances from the fulcrum?

 

[haruspex]

Im sorry i get what your trying to say but i just can't relate that to help me because in my mind this is how I am working it out Στ=τ(folcum) + -τ(rectangle) and the rectangle is mg and i know the net force is 0 but i don't get what you are trying to say ? I am sorry for being so helpless i just don't understand this at all

There are two equations available here (since there are no horizontal forces). One is that the net vertical force is zero, and the other is that net torque is zero. In principle, it doesn't matter what point you choose as the axis for calculating torque. But, as gneill wrote, choosing that point wisely can make the solution easier.
In this question, you not care what the force at the fulcrum is. If you choose the fulcrum as the axis for calculating torque then that unknown force does not feature in the torque equation. This will allow you to solve the question without considering the balance of vertical forces. If you choose any other point then the force a the fulcrum will feature in the torque equation, and you will have to use the vertical force balance equation as well in order to get a solution.
So, what is the torque about the fulcrum from the rectangular block?
What is the torque about the fulcrum from the beam?

 

[Julian3]

There are two equations available here (since there are no horizontal forces). One is that the net vertical force is zero, and the other is that net torque is zero. In principle, it doesn't matter what point you choose as the axis for calculating torque. But, as gneill wrote, choosing that point wisely can make the solution easier.
In this question, you not care what the force at the fulcrum is. If you choose the fulcrum as the axis for calculating torque then that unknown force does not feature in the torque equation. This will allow you to solve the question without considering the balance of vertical forces. If you choose any other point then the force a the fulcrum will feature in the torque equation, and you will have to use the vertical force balance equation as well in order to get a solution.
So, what is the torque about the fulcrum from the rectangular block?
What is the torque about the fulcrum from the beam?

Im sorry for the late reply and i just want to say thank you for attempting to help me and i did get it done with the correct anwsers but the amount of confusion i was in and the help i needed this would have had over 200 replies before i got the anwser right but thanks for trying to help me i appritate it