general physics lab

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Pre-lab #6 doesn't answer the question. I don't understand the calculation of initial velocity in pre-lab #7. #9 should not be 45 degrees.

The parameters of the experiment appear to vary at random. You should have two angle and three vertical distances. I don't see any calculations whatsoever. I don't see any comparisons of theoretical or experimental values. Please resubmit this report.

Purpose

The purpose of this lab is to test the 2-d kinematics equations.

Pre-Lab

1) In the absence of air resistance, which of the five other parameters affect the range? How do they do so (does an increase in the parameter increase the range, decrease the range, or is it more complicated)?

Answer: In the absence of air resistance, five other parameters which affect the range are angle, initial height, initial speed, mass and diameter.

By increasing the angle while keeping other parameters constant, the range increases up to angle 45o and after that it decreases. Hence, this elucidates that the range is maximum at angle 45o.

By increasing the initial height while keeping other parameters constant, the range increases and vice versa.

By increasing the initial speed while keeping other parameters constant, the range increases and vice versa.

By increasing the mass while keeping other parameters constant, the range is unaffected which means that range does not depend upon mass.

By increasing the diameter while keeping other parameters constant, the range is unaffected which means that range is independent of diameter.

2) In the presence of air resistance with a constant drag coefficient, which of the five other parameters affect the range? How do they do so (does an increase in the parameter increase the range, decrease the range, or is it more complicated)?

Answer: In the presence of air resistance with a constant drag coefficient, five other parameters which affect the range are angle, initial height, initial speed, mass and diameter.

By increasing the angle while keeping other parameters constant, the range increases up to angle 45 o and after that it decreases. Hence, this illustrates that the range is maximum at angle 45 o.

By increasing the initial height while keeping other parameters constant, the range increases and vice versa.

By increasing the initial speed while keeping other parameters constant, the range increases and vice versa.

By increasing the mass while keeping other parameters constant, the range is unaffected which means that range does not depend upon mass.

By increasing the diameter while keeping other parameters constant, the range decreases because as the diameter increases, the air offers more resistance to the object.

3) Perform a test with air resistance on, then repeat the test with air resistance off. Sometimes you will get a similar range (air resistance is negligible) while other times you will get a very different range (air resistance is significant). Try this under a wide variety of conditions. Then complete the following sentence: air resistance is negligible when …

Answer: Air resistance is negligible when we are talking about varying the angle parameter. With or without air resistance, the range is not affected significantly which means that air resistance has a negligible effect on angle and hence range.

4) Remove the air resistance. Place the cannon and the target 24 meters apart at the same height . Use a kinematics equation from the text or tip sheet to find an angle and initial speed that will hit the target. Show your work below. Did your prediction work?

Given:

Δx = 24m

Vf = 0 ay = -9.81 m/s2

Solution:

From Kinematic equations we know that;

Vf2 = Vo2 + 2ayΔx

(0)2 = vo2 + 2(-9.81) (24)

Vo = 21.68 m/s

To find the range of a projectile we know that;

After putting the values (R=24m)

ϴ = 15.01˚

Prediction did not work perfectly. The range obtained from initial velocity 21.68 m/s and angle 15.01˚ was 28m instead of 24m.

5) Keep the air resistance off. Choose a non-zero initial height. Find (through guess and check, not kinematics) and record the angle of maximum launch distance. Is this what you expected?

Answer: Keeping the height set to 5m and initial velocity 10 m/s, the angle of maximum launch distance (14.5meter) is 35˚. I expected that the maximum range would be obtained at angle 45˚ but that was not true after performing simulation.

6) Add the air resistance and select baseball. The world record baseball throw on level ground was reported[footnoteRef:1][footnoteRef:2] as 445 feet and 10 inches at an altitude of 1040 feet (this is not the initial or maximum height of the throw; it merely affects the air resistance). What was the minimum speed (in both m/s and mph) and optimal angle of this throw according to the simulation? You will simply need to use guess and check as the constant acceleration kinematics equations do not apply to this situation with significant air resistance. Note that will need to estimate a plausible initial height for the release. Note also that the simulation can’t take into account tailwind and ball spin, so your estimate of launch speed will be off. [1: http://www.baseball-almanac.com/recbooks/rb_guin.shtml (October 8, 2015)] [2: https://prestonjg.wordpress.com/2009/12/04/the-history-of-the-record-for-baseballs-longest-thrown-a-tale-that-involves-john-hatfield-honus-wagner-sheldon-lejeune-don-grate-rocky-colavito-and-glen-gorbous-among-others/ (October 8, 2015)]

Answer: According to Simulation, after hit and trial method, the Minimum speed obtained is 70 m/s or 156.586 mph whereas the optimal angle of this throw is 45o. According to the given statement, the throw would need a plausible initial height for the release, so I selected 5m as the initial height in the simulation.

Raw Data, Initial Uncertainty Estimation, and Observations

In Physics, like every other experimental science, one cannot make any measurement without having some degree of uncertainty. We measured the vertical and horizontal distances with a tape measure. The tape measure appeared to be worn, but this does not seem significant. The tape was slightly curved in the middle when fully extended. There might be some uncertainty in bubble level which checks the surface to be horizontal. The ground was not level, so the measured approximate length depended on where we placed the end of the tape. The ball may have picked up some dirt particles for subsequent drops. The scale limit of the device is 1 mm or 0.0393701 inches, so we can estimate the uncertainty in each trial reading.

Conclusion and Acknowledgments

So basically, the experiment was done to test the 2D kinematic equations and concluded that the range is affected by the angle and initial velocity of the projectile with or without air resistance. However, the range is independent of diameter without air resistance, whereas it decreases with increase in diameter of the object to be projected. The mass of the object is also not dependent on the range.

The predictions done in simulation did not perfectly matches with the results obtained from Kinematic equations. However, the results obtained are quite close. Our vertical and horizontal length calculations were imprecise since we used a tape measure on a rough ground surface. An experiment on a perfectly leveled surface would eliminate this problem.

I would like to acknowledge Galileo for his experiments on Projectile motion and the lab staff who helped me performing the experiment.