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Design and conduct an experiment that graphically determines whether drag force is proportional to the velocity of a falling object or proportional to velocity squared.

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Introduction

Problem statement: design and conduct an experiment that graphically determines whether drag force is proportional to the velocity of a falling object or proportional to velocity squared.

Independent variable:Mass

Dependent variable:Distance Fallen

Literature value: The literature value is comparison to the first trial’s height.

Research Question: How is the drag force (mass * gravity) proportional to the velocity (distancefallen = velocity * time) or to the velocity squared?

Hypothesis: If the mass of the object increases by a factor of x, then the drag force will be proportional to the velocity because drag force is opposite of the gravitational force so if the formula for gravitational force is mg = W. Then as the mass increases by an x factor, the gravitational force will increase by an x factor. The opposite of the gravitational force is the air drag so then W = k * v. The velocity is similar to the mass and k is the drag force coefficient. So the formula shows if the drag force increased by a x factor then so will the velocity indicating it is proportional.

Background information: The experiment is to determine if the drag force is proportional to the velocity or velocity squared.

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Middle

 .5

Time (s)

154

1.12

154

1.08

154

1.08

Relevant Formulas Used In The Experiment:

Relevant formulas:

W=m*g = v*k

W = weight

M = mass

G = gravity

V= velocity

K = Drag coefficient

D = v*t

D = distance

V = velocity

T = time

W = m*g = (v^2) *k

W= weight

M = mass

G = gravity

V = velocity

K = drag coefficient

Qualitative/Quantitative data:

The coffee filter with more dropped to the ground faster comparison to the first one.

Processed Data for the Experiment:

Labels

Position (m)

Time (s)

Estimated position (m)

Actual position (m)

Velocity (m/s)

Drag (

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Conclusion

velocity squared * surface area * ½ * drag force coefficient) is dependent on velocity squared.

The procedures are valid because they proved it was proportional to the velocity squared. One of the systematic errors was the ruler. To avoid, this error – one can use a magnifying glass to measure to the millimeter point. The systematic error increased the value by .05m. This is the uncertainty of the results. This is not accurate but precise because the results are similar but they are not accurate because they are off by .05m.

Improvements that can be made in the lab are the use of better equipment such as a computerized system that will measure the velocity at each point instead of when it only hits the ground. The procedures do not have to be manipulated because they proved the theory that air drag is based on velocity squared. The suggestions to improve the systematic error would be to use a magnifying glass to better see the lines on the ruler.

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