Interactive Lecture Demonstration 6 – Atwood's Machine

An "Atwood's machine" consists of two objects connected by a string that runs over a pulley. In the beginning of this demonstration, one of the objects will be hanging in the air by the string; the other object will be sitting on a box. The mass of the hanging object is 0.6 kg, the mass of the object on the box is 1 kg.

Throughout this activity you will be drawing force diagrams. Remember the rules that we learned in ILD5 yesterday for drawing such diagrams !

1. Draw a diagram of the situation.

2. Predict what the tension in the string must be for this situation. Use a force diagram (for an appropriately chosen object) to justify your answer.

After you have predicted the tension, compare your answer with the tension as measured by a pull scale. Were you right ?

3. Now predict what the force of the box on the second mass must be. Again use a force diagram for an appropriate object to justify your answer. This kind of force, from a surface pushing on an object in contact with the surface, is called a "normal force." The word normal means perpendicular in this context – the normal force is always perpendicular to the contact surface.

4. How could we measure the normal force of the box on the second mass ? Compare your predicted value for the normal force with the value measured in class once we measure it.

Next, the box will be removed from underneath the second mass. The system will accelerate once that happens. In the rest of this activity, we will calculate the system's acceleration and the tension in the string while the system is accelerating, using Newton's Second Law. We will follow a procedure that can be used to solve any problem that we will encounter involving Newton's Second Law.

5. Before beginning our calculation, predict what you think the tension will be when the system is accelerating. Will it be equal to, more than, or less than the tension was when the system was in equilibrium (i.e. not accelerating) ? Justify your answer by 1) labeling on the diagram the direction of each object's acceleration and 2) drawing force diagrams for each object in this new situation. Your force diagrams should show you (roughly, at least) what the tension must be.

6. Now we will actually calculate the tension. To do this, first choose a positive direction for each object. You MUST choose the positive direction to be the direction of the object's acceleration – otherwise, the whole rest of the procedure will not work. Draw your positive directions directly on your diagram. Next, write Newton's Second Law for each object. Do this in the form F_net = (sum of forces including appropriate directional signs) = ma. You will need to fill in the (sum of forces including appropriate directional signs) by looking at your force diagrams. You should be able to simply read a force diagram and write down the forces that it shows, including a + sign for every force that points in the positive direction and a – sign for every force that points in the negative direction. Write your two net force equations below:

7. Now you have done all of the physics there is to do. The rest of the problem is algebra. Find a way to solve for the unknown that you want. You have two net force equations and two unknowns (tension and acceleration). In this problem, let's solve for the acceleration first. Do that now. AFTER you have derived your formula symbolically, substitute in numbers with units and get your answer. Is your answer reasonable ? Could you have predicted roughly what the acceleration would be ?

8. Now let's solve for the tension (you may substitute in the number you got for the acceleration already, since now that is a "known" quantity). How does your answer compare with what you predicted ?

9. Now watch the system as it accelerates. Can you read the value of the tension from the pull scale while it's accelerating ? Is it close to what you calculated/predicted ?