Lab 6 - Atwoods Machine and N2 Instructions

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Physics

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May 13, 2024

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Lab 6 – Atwood’s Machine & Newtons Second Law PHY110 Lab – General Physics Lab I Vernier/Video LAB Objectives 1. Measure the acceleration of the Atwood’s Pulley System using two different methods 2. Determine the total mass of the system by plotting the Net force vs. Acceleration 3. To verify Newtons Second Law stating that the Net force is proportional to the acceleration 4. Determine the friction that acts on the system

Equipment List:  Vernier Software  Atwood’s Machine – Full Video  Vernier Data Files o Atwood’s Machine mass diff 4g o Atwood’s Machine mass diff 8g o Atwood’s Machine mass diff 12g o Atwood’s Machine mass diff 16g o Atwood’s Machine mass diff 20g o Atwood’s Machine mass diff 24g  Stopwatch (easy touch-based stopwatch) Introduction Newtons Second Law of Motion can be modeled using a system called the Atwood’s Machine (as shown in Figure 1). It consists of two masses at the end of a thin string that passes over a pulley. Figure 1 – Atwood’s Machine Apparatus The difference in the two masses generates a net force on the system, causing the two masses to accelerate. According to Newtons Second Law, F net = m a (1) Where m is the mass of the system in kg, a is the acceleration in m/s 2 and F net is the net force in Newtons, the acceleration of the system is directly proportional to the Net force of the system. The Net Force of the system can be derived from the free-body diagram. Lets assume that m 2 is larger than m 1 . Therefore the resulting free-body diagram is modeled in Figure 2 where m 2 is pulling the system downward.

Figure 2 – The free-body diagram of m 1 and m 2 , assuming m 2 is pulling the system downward. T represents the tension in the string and the bottom force is the weight, or mg of each mass. The tension of the string is the same throughout, therefore the tension T in the free-body diagram for m 1 is the same as the tension in the free-body diagram for m 2 . The free body diagram gives the net force for each mass T − m 1 g = m 1 a and m 2 g − T = m 2 a (2) One can add the two equations simultaneously to eliminate the Tension variable (also unknown in the experiment) and to combine the equations into one m 2 g − m 1 g = m 2 a + m 1 a (3) The expression can be reduced down to ( m 2 − m 1 ) g = ( m 2 + m 1 ) a (4) Written this way, the expression models Newtons Second Law. The Net Force on the left is the difference in weight and on the right, the m is replaced by the combined masses ( m 2 + m 1 ) and a remains the net acceleration of the system. In the lab setting the masses can be measured with a triple beam balance or scale, and the acceleration can be measured either using kinematics or through Vernier Smart Pulley photogate measurement. The pulley will impart some friction on the system. We can rewrite equation 4 to incorporate the friction on the system with ( m 2 − m 1 ) g − f = ( m 2 + m 1 ) a (5) The friction can be added to the right side of the equation to model a linear relationship similar to y=mx + b. In this case, the y-axis will be the Net force, ( m 2 − m 1 ) g , the x-axis will be a . This leaves the slope as the ( m 2 + m 1 ) or the total mass of the system and the y-intercept will represent the frictional force implied on the system. ( m 2 − m 1 ) g = ( m 2 + m 1 ) a + f (6) The acceleration in this lab will be measured two ways. The first way is through the kinematic equation

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