Introduction/Background

In this lab we will learn about pulleys and also work. First of all, and ideal pulley simply redirects a tension force, without changing its magnitude. That is all. So the magnitude of the tension force on a

rope just before it goes over a pulley is the same as the magnitude of the tension force on the rope right after it goes over a pulley. An ideal pulley has negligible mass, no friction on its axle, and the rope does not slip on the sheave (sheave is what we call the actual wheel in the pulley).

Work has a very definite meaning in physics. It is the amount of energy that forces add to the system we are considering (often a single mass). The work done by a constant force F acting on the system as the system moves by a position vector d(or more properly, the place where the force is applied on the system moves a distance d) is W = |F| |d| cos , whereis the angle between the distance vector d and the force vector F. Thus for instance, if there is a 100 N friction force (which always opposes motion) acting on a block, and the distance the block moves is 10 m, then the work done by friction is W = (100 N) (10

m)cos(180^o) = -1000 Nm = -1000 J, where J stands for Joules, which is a kg m²/s². The negative sign comes from angle between the force and the distance, which are in opposite directions, and this means the friction force takes energy from a system, which makes sense.

Description of Experiment In your labpaq kit, there should be a pulley similar to the pulley picture in Fig. 1.There should also be a spring scale, and a block with a hook attached to it that was used in the friction lab.

Fig 1(a-c) (left to right): Fig 1a shows the setup for parts 2 and 3.Fig 1b shows the spring scale and zeroing tab. Fig 1c shows the setup for the pulley for part 1.

There are 3 parts to this experiment.

1. In the first part of this lab, we want to see if the pulley just re-directs the tension force in a string without changing the magnitude of the force. Hang the wooden block from the spring scale, and record the block's weight in N (make sure the spring scale reads zero when no mass is hung on it. Pull the metal tab shown in Fig. 1b to do this). Tie a loop of string around something that is at least a meter above the ground. In Fig 1c. the loop of string is tied around a doorknob. Hook the pulley on this string. Thread about 1m of string over the sheave of the pulley. Attach one end of this string to the wooden block. Tie the other end of the string in a small loop, and attach the spring scale to it (make sure the spring scale has been re-zeroed, so it reads zero when there is no mass on the other end of the string).What does the scale read now? Is this weight consistent

(use the z' test in the uncertainty handout) with the weight of the block when it was directly attached to the scale. Pull down on the spring scale, raising the block very slowly and at a constant speed.Does the spring scale's reading change much from when the block was at rest?

1. In the second part of this lab, we want to test our understanding of pulleys and of Newton's second law. First mass the block and the pulley on the spring scale. Find a length of string that is about 1 m long. Tie one end of this string to something fairly solid like the doorknob in Fig. 1a. Put the pulley over this string, so the sheave of the pulley is on top of the string, and the other end of the string goes straight back up. Hang the block directly from the pulley (there should be 2 hooks on the pulley, hook one of them to the block). Predict, using Newton's second law, what a spring scale that is attached to the free end of the string should read (with uncertainty). Attach a spring scale to the free end of the string andmeasureits reading (with uncertainty). Is your prediction consistent with your measurement (be quantitative)? Explain any discrepancies if you can.
2. In this part, set up the pulley, spring scale, and block as in part 2. Slowly pull the free end of the string up 30 cm, measuring the tension force. This raises the block some. How much work was done by this tension force? How much work was done by gravity on the pulley/block system? The Work-Kinetic Energy theorem states that the sum of the work done on a mass is equal to the change in kinetic energy of the mass. If the mass was moved very slowly, at a constant speed, there is no change in kinetic energy. Is the sum of the work done by gravity and by the tension force in the string zero to within uncertainty? Explain any discrepancies if you can.

Question:

If the ends of the string in part 2 were not vertical, but instead made an angle of 30-degrees with respect to vertical, and the pulley and block together had a mass m, what would be the reading on a spring scale attached to the free end of the string the pulley is on?