Motion in Free-Fall Lab Report PDF

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Summary

The motion of a body falling freely under gravitational attraction will be examined, and from the measured rate at which the velocity changes with time the acceleration due to gravity (g) will be determined....

Description

Benjamin Kelley PHYS.1410 (Physics 1) Section 809

Instructor: Chaminda Ranathunga Date of Experiment: 9/25/2018 Partners: Jeffrey Hyde

Experiment:

Motion in Free-Fall

Objective:

Prove the acceleration of a mass in free-fall is the force of gravity by calculating time and velocity.

Introduction

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Whenever a body is acted upon by a net force, the force causes the body to accelerate. If the force has a constant magnitude, then the acceleration will also be constant. When a body is simply dropped, it will enter free-fall where it will fall towards the center of the earth due to the force of gravity. If the body is close enough to the surface of the earth, then the force of gravity will be relatively constant also meaning the gravitational acceleration will be constant. Acceleration is defined as the rate of change in velocity over a certain time and can be represented by this equation: a = (v-vo) / t v = vo + at (a = acceleration, v = final velocity, vo = starting velocity, t = time) However in this experiment we don’t have the value for acceleration. So, we must instead refer to the equation for average velocity which is total distance travelled over total time. v =s/t

(s = total distance) For any motion that is uniformly accelerated the average velocity is just the mean of starting velocity and final velocity: v = (vo + v) / 2 Now if we combine each of these equations we arrive at the final relationship between displacement and time: s = vot + ½at2

Apparatus and Procedure

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Equipment Used: ● Vernier caliper ● Meter stick ● Masking tape ● Paper tape ● Hooked mass ● Timer/hammer apparatus

Apparatus Diagram

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Tape Diagram

Description of Experiment: The first thing that needs to be done is cut a piece of paper tape to 60-80 cm long and attach a piece of masking tape to the end. Then force a hooked mass through this masking tape. Next, run the tape through the slot on the timer. Turn the hammer on to 40 Hz and let go of the tape. When you see the dots on the tape, mark the first clear dot as dot 0. Label all of the following dots as dot 1, 2, 3, etc. Measure the total distance between dot 0 and the next dot (1, 2, 3) with a meter stick and label it as S1, S2, etc in the data table. Next use the vernier caliper to measure between each individual dot (dot 1 to dot 2, dot 2 to dot 3, etc) and label these as delta S1, delta S2, etc. Be sure to mark the time between each dot as 1/40 second.

Results and Analysis

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Page 5: Table of t, Sn, Delta Sn, and Average Velocity Page 6: Instantaneous Velocity vs Time Graph Page 7: Displacement vs Time Graph Page 8: Table of t, Velocity (from graph), and Average Velocity

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Analysis The line of best fit for the Instantaneous Velocity vs Time graph is a straight line that represents the equation v = vo + at. This means that the y-intercept of the line is the starting velocity of the mass and the slope of the line is the acceleration. We can select two points on the line and find the slope with said points. I used the points A(5/40,153) and B(10/40,277). slope = (VB - VA) / (tB - tA) slope = (277-153) / (10/40 - 5/40) slope = 124/0.125 slope = 992 So the slope of this line and thus the acceleration of the mass is 992 cm/s 2 or in SI units it would be 9.92 m/s2. Also from the graph vo would approximately be 36 cm/s or in SI units 0.36 m/s. Taking into account the accuracy of the points plotted on the graph, we can say the uncertainty of velocity is +/- 1 cm and no uncertainty of time since we know each interval is 1/40 second. This then makes the uncertainty of acceleration +/- 1 cm or +/- 0.01 m in SI units. The curve of the Displacement vs Time graph shows the quadratic increase of displacement, which makes sense because the derivative of this curve would be the straight line of increasing velocity. By two points on the graph we can test the accuracy of this drawn curve. I selected the point at t = 5/80 and 25/80. The tangent lines at these points are the instantaneous velocity at that time. At t = 5/80, I estimated a velocity of 98.8 cm/s when the actual is 116 cm/s and at t= 25/80 I estimated a velocity of 320 cm/s when the actual is 328.8 cm/s. The general ballpark of the estimations show that the Displacement vs Time graph is fairly accurate as well as the Instantaneous Velocity vs Time graph since my calculations are fairly accurate as well.

Discussion

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After completing the experiment and analyzing the data, it appears that the results are pretty accurate to the claim that gravity is the only force working on an object in free-fall. As for experimental uncertainties, the only kind that I believe may have occurred an error in dropping the paper tape through the apparatus. It may be possible that the tape got caught on something as it was being pulled through the timer/hammer apparatus. This would then cause an inaccurate dot on the tape that would have thrown off the graph. As for difficulties, the only kind that I really had was determining which dot on the tape to mark as dot 0 as well as getting accurate measurements on the total distance between all of the dots. Other than that, this experiment ran smoothly.

Conclusion In conclusion, we can confirm that when a body is in free-fall the only force working on that body is gravity. This then means that the only constant acceleration on that body is gravitational acceleration, causing its velocity to increase at a constant rate. In addition with this discovery, we can also conclude that the velocity of an object can be found using the equation: v = vo + at. Again, showing that the body’s velocity will increase at a constant rate over time.

Questions

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1. What is the difference between your value of g determined from the Instantaneous Velocity vs Time graph and the accepted value? What do you consider to be the principal sources of experimental uncertainty in your measurement?

I would consider the primary source of error to be the graphing of the best fit line on the graph.

2. If the plummet had been given an initial downward push instead of being released from rest, what effect (if any) would this have on your measured value of g? This would have no effect on the measured value for g since this push is not constant and is only applied at the start. This force would give the object a starting velocity greater than 0 and leave acceleration to be the same.

3. From the Displacement vs Time graph what are your conclusions concerning the dependence of displacement on time for a body in free-fall? What is the functional relationship between displacement and time for this motion? The displacement of a body in free-fall is directly related to the time that has passed while the object is in free-fall. These two quantities have the functional relationship of

v t = s,

meaning that as time increases so does the displacement of the body.

4. Should the tangent to your displacement curve at the point selected to be s= 0 and t = 0 be horizontal? Explain your answer carefully.

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As defined kinematically, the body at time = 0 and displacement = 0 has no velocity. Since the tangent of the displacement curve represents the instantaneous velocity at that point in time, the tangent curve at time = 0 should be horizontal, meaning that the body has no velocity at that point in time....