Question

Torque and Equilibrium

You are in a class titled Introduction to Artistic Expression, and your final project must be completed in class. You know that you will be given three objects and two boards to work with to create two separate displays. You also know that you must arrange the objects on the boards so they balance on a tiny pedestal. Once completed, one display will be a single object resting on a board balanced on top ofa pedestal; the other will be two objects resting on a board balancedon top of a pedestal.You do not know precisely what objects you will have to work with, but you decide to do the calculation for balancing the displays before class so that you will have more time to think about the artistic presentation in class. You decide to make two models using a mass set and a meter stick in order to test where the objects should be placed in order to balance them for each setup.

Equipment:You have a meter stick and a mass set to test out your models.

Two mass system:

1.Draw a picture for the two-mass system(two masses resting on a meter stick that is balanced on a point), assuming that there are two different masses involved. Since there are many ways you could do this, for purposes of this pre-lab, also assume that both masses are placed at the same distance from the middle of the meter stick, on opposite sides. Identify and label the quantities that are relevant and that you can measure in this problem, such as masses and lengths.

2.Select a coordinate system, including an origin, and draw a free-body diagram ofthe board thatincludes distances from the balance point for each force.On your diagram, identify each force on your system.

3.Using your coordinate system,write down an expression for the net torque on the system in terms of your distances and masses. What is the net torque

when the system is in equilibrium?

Answer 1

Here is the Picture of a setup including two masses and a pivot point

Here is the free body diagram showing all the forces and distances.

Now, There is very important thing to note down while finding torque. The clockwise torque is negative and counter clockwise torque is positive.

Torque = force*perpendicular distance

Now, if we are to find torque created by each mass about point marked as O , then we have

Torque ( from mass m1) = m1*g*d1

Torque (from mass m2) = - m2*g*d2 (notice the negative sign is due to clockwise torque)

Now, if the system is considered to be in equilibrium, then

?Torque_net = Torque₁ + Torque₂

?Torque_{net =} m1*g*d1 - m2*g*d2

?Torque_net = 0 ( In equilibrium)