Formal Lab Gravitaional Acceleration

Lab #5: Gravitational Acceleration

Preparation: In preparation for the first part of this lab involving the Atwood's machine our team started by discussing the effects of the masses on the results of the machine as requested in question 1 of the lab manual. We believe that if the two masses were equal there would be no motion of either of them when released. However we believed that if the two masses were not equal, the heavier mass would fall downward pulling the lighter mass upwards.

Below as requested by question 2 is a free body diagram of both situations

Masses Equal

Masses Unequal

The tension on mass 1 is equal to the tension in mass 2 due to the same string attaching both masses and is shown mathematically above in the section where the masses are equal. In the second part gravity is solved for.

We also believe that the difference between the two masses will affect the acceleration in a linear matter as requested in question 3.

In preparation for part 2 we started by answering question 4 on which graph best describes freefall based for distance vs. time. We believed graph (b) showed this and is shown below.

Our rational for this was that the object in free fall is undergoing a constant acceleration meaning its velocity will increase with time. This is shown on graph (b) by the increasing slope with time, and is the only graph to have its slope increase with time. Graph (a) has constant slope and graph (c) has its slope decrease with time.

For question 5 which asked for the best velocity vs. time graph we believed that graph (a) is the best graph.

Our rational for this was that because the object is under constant acceleration the velocity will increase at a constant rate. Graph (a) shows this while graph (b) shows constant velocity and graph (c) shows decreasing velocity.

For question 6 which asked for the best acceleration vs. time graph we believed that graph (b) shows this the best.

Our rational for this was that the object is under constant acceleration. Only graph (b) shows a constant acceleration. Graph (a) shows decreasing acceleration while graph (c) shows increasing acceleration.

Procedure: Our procedure for part 1 is the following: First we measured the masses of both sides of the Atwood's machine and record these values. Next we held the smaller mass on the ground and measured the distance from the ground to the bottom of the larger mass, calling this value "s". Next we released the smaller mass and timed how long it took the larger mass to fall and recorded this as "t". We did this 4 times to allow each member of the team to do this. We then averaged the value for time and solved for gravity and the associated error.

For part 2 our procedure was the following: Using a device to determine how long it takes a ball to drop from 1 sensor to another we started by measuring the distance from the bottom of the ball to the top of the sensor on the ground calling this value "s". We then turned the machine on, reset it and allowed the ball to drop by releasing the pressure on the ball holding it to the elevated sensor. We recorded the time given by the machine calling it "t", and repeated for 4 attempts. We then averaged the value for time and solved for gravity and the associated error. We did this process with 2 different heights.

For part 3 our procedure was the following: Using a pendulum we started by recording the distance from the center of mass of the ball, to the top of the pendulum calling this "L". We then let it oscillate in a straight line for 100 periods and recorded this time. We then divided this time by 100 to get the time for 1 period "t". We then solved for gravity and the associated error. We did this process with 2 pendulums.

Data: Part 1: (Atwood's Machine)

Mass 1: 197.35±.05 g

Mass 2: 188.90±.05 g

Distance (cm) Time (sec)

237.00±.05 5.81±.1

237.00±.05 5.62±.1

237.00±.05 5.91±.1

237.00±.05 5.78±.1

Part 2: (Free fall)

First Height

Distance (cm) Time (sec)

179.60±.05 0.612±.0005

179.60±.05 0.614±.0005

179.60±.05 0.625±.0005

179.60±.05 0.615±.0005

Second Height

Distance (cm) Time (sec)

49.70±.05 0.319±.0005

49.70±.05 0.319±.0005

49.70±.05 0.319±.0005

49.70±.05 0.317±.0005

Part 3: (Pendulum)

Distance (cm) Time for 100 Swings (sec) Time for 1 swing (sec)

236.00±.05 308.85±.1 3.0885±.001

128.00±.05 227.91±.1 2.2791±.001

Analysis: Part 1:

To determine the gravity based on the Atwood's Machine we started by finding the average time for the large mass to fall. The calculations for this are below. We estimated our error for time to be .1 seconds based on reaction time of the team members.

Now after converting our values for m into kg and for s into meters we plugged the value for t, s, m1, and m2 into the below equation to give us our gravity value.

Finally