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# Atwood 2 - (Newton's Second Law and the Conservation of...

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THE ATWOOD MACHINE (Newton's Second Law and the Conservation of Energy) OBJECTIVE: To study the relation of masses and accelerations. METHOD: Consider the Atwood machine shown in Fig. 1. A pulley is mounted on a support a certain distance above the floor. A string with loops on both ends is threaded through the pulley and different masses are hung from both ends. The smaller mass is placed near the floor and the larger mass near the pulley (the pulley can be adjusted to the appropriate height). The masses are then released and the time for them to exchange places is measured. Part 1. Newton's Second Law THEORY: Consider the larger mass, m 1 . There are two forces acting on it. One is the force of gravity, W 1 = m 1 g , pulling it downward. The other force is the tension in the string, T 1 , which is pulling it upward. Taking up to be the positive direction, Newton's 2nd Law gives Σ F y = - m 1 g + T 1 = m 1 a 1 . (1) Now consider the smaller mass, m 2 . Again there are two forces acting on it. One is the force of gravity pulling it downward. The other force is the tension in the string pulling it upward. Thus, Newton's 2nd Law gives Σ F y = - m 2 g + T 2 = m 2 a 2 . (2) Because the string is attached to both masses, a 2 = - a 1 = a . We now assume that the string’s mass is much less that either of the hanging masses and that the pulley does not rotate as the masses move. This allows us to say that T 1 = T 2 = T . (In reality, the pulley does rotate and the tensions can’t be equal if it rotates.

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