lab report 3 - PHY2053L

Cristian Acuna Vasquez 01/27/2020 PHY2053L Title: Atwood’s machine Purpose: To investigate and validate Newton’s seconds law of motion utilizing an Atwood’s machine. Background Information: Force is a vector and measured in Newtons. There are different types of force, such as gravity, friction, applied force, normal force, etc. Normal force is perpendicular to the surface and is exerted by the surface. The force of gravity is equal to an object’s mass multiplied by gravity. The sum of the forces, or net force, is equal to an object’s mass multiplied by acceleration. Tension is the force applied by a rope, string, or cable. Tension is the same throughout a string. Thus, there is only one value for tension in this lab. The Atwood machine consists of a pulley, which connects two masses. When these masses are unequal, the system will accelerate in the direction of the larger mass. The Atwood machine is used in experiments to verify the mechanical laws of motion with constant acceleration, which is a valuable tool for purpose of this experiment to verify the predictions of Newton’s law. This law predicts that the acceleration should be proportional to the difference between the masses and proportional to their sum. A = [ (m 2 -m 1 ) / (m 1 +m 2 ) ] g. In this lab, the acceleration of masses will be identified both experimentally and theoretically. The system will begin at rest. Therefore, having recorded the distance traveled and the time it took to do so, the experimental acceleration will be calculated using kinematic equations.

Materials: Computer, Vernier Computer interface, Logger Pro, Vernier Photogate with Ultra pulley attachment, mass set, String 1.2 m long. Procedure: Setting up the Atwood’s machine apparatus with proper pulley and string. Connect the Photogate with Ultra pulley to a digital port of the interface. Arrange a collection of masses on m 2 and m 1 . Tie the heavier mass to one end of the string. Lace the other end of the string through the pulley. Tie the lighter mass to the other end of the string. Turn on the machine Photogate timer. Release weight and collect data via Vernier computer interface. There will be 5 trials with increasing total mass, which is same amount of mass added to each weight and another 5 trials with increasing mass difference, in which we will move masses from one side to the other thus we will keep total mass the same. Data: Part I Trail M 1 (g) M 2 (g) Acceleration (m/s s ) M diff (m1-m2) (g) M t (g) 1 20 20 0.09 0 40 2 10 30 4.2 20 40 3 30 40 1.0 10 70 4 20 50 3.7 30 70 5 30 50 2.2 20 80 Part II Trail M 1 (g) M 2 (g) Acceleration (m/s s ) M diff (m1-m2) (g) M t (g) 1 10 20 2.7 10 30 2 20 30 3.7 10 50 3 30 40 1.0 10 70 4 40 50 2.9 10 90 5 50 60 0.8 10 110

Based on the graph, the relationship between constant total mass and acceleration in an Atwood’s machine would be directly proportional. 4. Plot a graph of acceleration vs m t using Part II.. What is the relationship between total mass and the acceleration of the Atwood’s machine?

O Based on the graph, the relationship between total mass and acceleration in an Atwood’s machine would be inversely proportional 5. Develop a single expression for the acceleration of an Atwood’s machine , combining the results of the previous two steps in the analysis. A = [ (m 2 -m 1 ) / (m 1 +m 2 ) ] g. Error analysis The majority of the sources of error were due to frictional forces. The mass of the pulley is only taken into account when the pulley is initially frictional. It basically affect every fragment of the system, which includes tension force, gravity to velocity and acceleration to time. The friction that causes is static, if we increase the mass of the pulley, it will affect the whole system by increasing the static friction. Also there were observers errors, as some teammates did not stop the program when each trial ended.