Question

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 of a pedestal; the other will be two objects resting on a board balanced. 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 have more time to think about the artistic presentation. 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. You will use a few masses stacked for the small pedestal.

One mass system:

1. Draw a picture for the single mass model. Select a coordinate system. Identify and label

the quantities you can measure in this problem, such as masses and lengths. The unknown

quantity in this problem is the locations of the mass in relation to the balance point.

2. On your picture, identify each force on your system. Draw a free-body diagram of the board that includes distances from the balance point for each force. For now, identify an arbitrary balance point for the system. (This is OK, you will use the condition of equilibrium to make the correct choice in a bit.)

3. Write down an expression for the net torque on the system. What is the net torque when the system is in equilibrium?

4. How many unknowns are there in your torque equation? Since we have too many unknowns to solve this equation, we need to add an additional constraint. Make the object mass twice the meter stick mass.

5. Solve the equation to find the equilibrium location of the mass.

Two mass system:

1. Draw a picture for the two mass system, assuming that there are two different masses involved. Select a coordinate system. Identify and label the quantities you can measure in this problem, such as masses and lengths. The unknown quantities in the problem are the locations of the masses in relation to the balance point.

2. On your picture, identify each force on your system. Draw a free-body diagram of the board that includes the distances from the balance point. For now, identify an arbitrary balance point for the system. (This is OK, you will use the condition of equilibrium to find how you need to correct your choice.)

3. Write down an expression for the net torque on the system. What is the net torque when the system is in equilibrium?

4. How many unknowns are there in your torque equation? Since we have too many unknowns to solve this equation, we need to add additional constraints. For the two mass system, we decide that the masses must be placed equal distances from the 50cm mark on the meter stick. Also, select your masses so there is at least 30g difference between them. You will need to discuss with your group what these constraints will actually be so you can just consider the quantities to be ‘known’ as you solve the system of equations.

5. Solve these equations to find the equilibrium location of the two masses.

Prediction

Write a formula for the equilibrium position of each mass balancing on each of the two meter sticks, in terms of masses and their distances from the balance point. Assume that all the masses are different. Identify the variables that are set by the group and the variable that is being measured.

Answer 1