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To determine the relationship between mass and acceleration when force is kept constant.

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Introduction

Kelvin Johnston Chua 12CD        Code: FM2B        05/ 10/ 03

        Mr. Kalsi

Aim:

To determine the relationship between mass and acceleration when force is kept constant.

Hypothesis:

I predict that the relationship between mass and acceleration will be inversely proportional to one another. Supported by the theory from Isaac Newton. He described the relationship of the net force applied to an object and the acceleration it experiences in the following way: the acceleration (a) of an object is directly proportional to and in the same direction as the net force (Fnet), and inversely proportional to the mass (m) of the object.

Apparatus: image00.png

  • Data logging software on computer
  • Pasco Trolley set
  • String
  • Pulley system
  • Hooks and weight [10g each]
  • 6 500g blocks

Variables:

Variables

Description

Units

Dependant

Acceleration of the cart

m/s2

Independent

Mass on the cart

kg

Constant

Friction of surface

Mass on hook

Incline of plane

Mass on cart

N/A

kg

cm

Methods:

  1. Record the weight of the cart and each of the weights.
  2. Then assemble the dynamic cart system as shown in the diagram above.
  3. Connect the string to the cart and place some weights on the hook hanging down, and record the mass of the entire hook [0.050kg]. Keep this constant through the experiment.
  4. Make sure that the plane is totally parallel to the table with no incline. Use the cart to test it, do not apply any force and see if it moves by itself.
  5. Make sure that the light sensor is functioning well that if something cuts through the light gate, the light should go off and then on again.
...read more.

Middle

3.26

0.0938

3.00

3.51

0.0837

3.25

3.75

0.0732

3.50

4.01

0.068

3.75

4.26

0.062

NOTE: For Average Acceleration, it is considered to be digital error. Which rounded of the last digit.

For example:

If the machine shows to 2 decimal points, 3.14 then the uncertainties for this are ±0.005 as the range of the data could go from 3.135 to 3.145.

As we could see that the data above [average acceleration] is all rounded up to 3s.f. And some has 2 decimal points, 3 decimal points and even 4 decimal points so the uncertainties may differ of 0.005, 0.0005 or 0.00005. But if we look closely only one of them is with 4 decimal points and the majority is with 3 decimal points, therefore I come up that the uncertainties for average acceleration is ±0.0005.

Summary of all the Error Uncertainties

Mass of
cart (kg)

Force

(N)

F= mg

Total Mass

(kg)


Average

Acceleration
(m/s
2)

± 0.025

± 0.025

± 0.05

± 0.0005

We used 10 weights. Each weight’s uncertainty is 0.005g.

And total uncertainty is 10 x 0.005 = ± 0.05g.

For example:

Cart and Hook + 8 weights = ± 0.005 + 9 x ± 0.005

                                  = ± 0.05g

Remember that this is the total uncertainty, which are the total mass’s uncertainties. But while you are doing addition the uncertainty are being added together. Since there are two things added therefore the uncertainty for each is now ± 0.025.

While since “g” has no uncertainty and now that I have said that the uncertainty for the mass hanging is ± 0.025, therefore there is no change in uncertainty during the multiplication is done.

Graph Data of x and y axis:

(x axis) Total 1/Mass = 1/m (kg)

Error Uncertainty is ±  0.05

(y axis) acceleration = a (m/s2)

Error Uncertainty is ± 0.0005

1.96

0.773

1.32

0.523

0.991

0.377

0.794

0.296

0.662

0.250

0.568

0.196

0.497

0.168

0.442

0.153

0.399

0.130

0.362

0.117

0.333

0.105

0.307

0.0938

0.285

0.0837

0.266

0.0732

0.249

0.0681

0.235

0.0620

...read more.

Conclusion

Modifications:

Of course if I did indeed do the experiment again I would have to take friction and air resistance into account. The way in which I would suggest to overcome this would be to use an air track. This would get rid the experiment most of friction though due to it being an air track there would still be some resistance from air molecules. Though this method, if one does not already own an air track, would be an expensive method.  But in this method you will encounter air resistance as well as a little bit of friction. But nothing could be done about the air resistance problem in this experiment due to the equipment and place to be done in the school laboratory.

However, the error may be reduced significantly if a greater range of testing for weights (kg) was used.

For example, tests can be made from 0.01kg and with intervals of 0.001kg for 20 (or even more) testing points.

Plus, to decrease the error or chances of getting unreasonable results, 7 (or more) runs should be performed for each testing point.

By increasing the range and repetition of testing may bring results closer to the literature value which will let F = ma, where the gradient will be closer to the force applied.

...read more.

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