Work Energy Theorem (Atwood s Machine)

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Ashley Lawrence
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1 Work Energy Theorem (Atwood s Machine) Name Section Theory By now you should be familiar with Newton s Laws of motion and how they can be used to analyze situations like the one shown here this arrangement is known as an Atwood s machine. It is assumed that there is negligible friction or inertia associated with the pulley. Since m 1 > m 2, m 1 will descend as m 2 ascends. In this experiment, we will use this apparatus to examine the Work Energy Theorem. This theorem states that the work W done by the resultant external force on an object is equal to the change in kinetic energy K of the object. W =K 2 K 1 = K (1) When solving problems such as these, it is important to clearly define the object for analysis. Here, we have three options: m 1, m 2, or the system of masses m 1 + m 2 (they are connected via the string). There are two forces on m 1, its weight and the tension in the string; this is also true for m 2. The resultant force on each mass is the difference in these two forces, but we would need to know the tension in the string in order to proceed. There are also two forces on the system, the respective weights of the masses. However, these may be combined into a single force (the difference in the weights). The system is constrained to move only around the pulley. The situation is analogous to two masses connected by a string sitting on a horizontal, frictionless surface. If m 1 experiences a greater force than m 2, then the system will accelerate in the direction of m 1. The resultant force on the system is just the sum of the two individual forces. Therefore, the work done on the system is W=Fd = m 1 g m 2 g d = m 1 m 2 gd (2) where d is the distance the system moves. If we let m 1 descend a measured distance y from rest (v o = 0), then the velocity it acquires is y= v o v f 2 t v f = 2y t (3) which can be used to determine the kinetic energy acquired by the system. K= 1 2 m 1 m 2 v 2 (4) Sp07 Page 1 of 5

2 Apparatus Table clamp, Right-angle clamp, Rod, Pulley, String, Hooked masses, Slotted Masses, Stopwatch, Meterstick, Triple-beam balance. Procedure Set up the Atwood s machine. The length of string should be such that when m 2 is sitting on the floor, m 1 will be not too far under the pulley. With m 1 held in this position, you can easily measure the distance that it will descend to the floor, and this distance will be reproducible for multiple trials. 1. Take a 200g hooked mass and measure its mass on the triple-beam. This will serve as m 2. Take another 200g hooked mass and place a 5g slotted mass on top of it. Measure the mass of this combination, which will be m 1. Record the masses in Table 1 for Trial Place m 1 and m 2 at different ends of the string and hold m 1 in place while m 2 sits on the floor. Measure the distance m 1 will fall to the floor (also the distance the system moves). Record this value. 3. Release m 1 and time its descent to the floor. Record the time and repeat for a total of five trials. Calculate and record the average time. 4. Calculate and record the resultant force on the system, the work done on the system, and the velocity and kinetic energy acquired by the system. Finally, calculate and record the percent difference between the work and kinetic energy. 5. Repeat Steps 1 4 with a 10g and a then a 20g slotted mass on m 1 (for Trials 2 and 3). Sp07 Page 2 of 5

3 Table 1 Work and Kinetic Energy Trial 1 Trial 2 Trial 3 Sp07 Page 3 of 5

4 Analysis 1. What is the average percent difference between the work and kinetic energy for all trials? 2. Based on your answer to Question 1, do you think the Work Energy Theorem was verified? Why or why not? 3. What do you think accounts for the difference between the work and kinetic energy? Sp07 Page 4 of 5

5 Pre-Lab: Work Energy Theorem (Atwood's Machine) Name Section 1. A resultant force of 3.00N acts on an object that undergoes a displacement of 250.0cm (in the same direction as the force). What was the work done on the object by this force? 2. Does it matter what the mass of the object is in Question 1; i.e., will this alter the work done on the object? 3. An object with mass of g starts at rest and has a final velocity of 2.50m/s. What kinetic energy did it acquire? 4. What does the Work-Energy Theorem say? Sp07 Page 5 of 5

Atwood s Machine: Applying Newton s Second Law (approximately 2 hr.) (10/27/15)

Atwood s Machine: Applying Newton s Second Law (approximately hr.) (0/7/5) Introduction A physical law is a statement of one of the fundamental theoretical principles that underlie our understanding of