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Forces Lab. I decide to investigate the relationship between the propelling force exerted on the weighted margarine tub and the distance travelled by the tub.

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Introduction

Title: Margarine tub investigation   Selina Wang

Title: Margarine tub investigation

Introduction:

This experiment is designed to investigate one factor affecting the distance travelled by a weighted margarine tub when it is propelled along a runway. I decide to investigate the relationship between the propelling force exerted on the weighted margarine tub and the distance travelled by the tub.

image00.pngIn this experiment, the propelling force is the gravitational force of those hanging weights and it is calculated by image01.png. The distance travelled by the weighted margarine tub is equal to the total forward distance (image04.png) minus the pulling distance, and the pulling distance is equal to the height from those hanging weights to the floor (h). Therefore image05.png.

Research question:

How is the distance traveled by a weighted margarine tub (d) dependent on the magnitude of the propelling force exerted on it (F)?

Variables:

Independent variable: The magnitude of the mass of the hanging weights.

*image01.png, this is how I link my independent variable to the magnitude of the propelling force exerted on the weighted margarine tub. Then I can further investigate the relationship between the propelling force and the distance travelled by the tub.

Dependent variable: The distance travelled by a weighted margarine tub

Controlled variables:

  • The total mass of the weighted margarine tub
  • The friction of the runway
  • The height from the hanging weights to the floor

Hypothesis:

As shown in diagram 1 above, the margarine tub and the hanging weights are connected by a string, therefore they are in the same system. Theoretically, the total energy in the system is conserved, which means the loss in the gravitational potential energy when the weights drop (PE) is equal to the kinetic energy gained by the weighted margarine tub (KE) which propels the tub to move. After the tub is propelled, the only horizontal force exerted on it is the friction between the tub and the runway (f), and it is the friction that slows the tub down and finally stops it. Therefore the kinetic energy gained by the tub is equal to the work done by the friction between the tub and the runway.

  • Formula rearrangements:

image31.png

image40.png

image50.pngWork done by frictionimage59.png

image68.png

image02.png

Alsoimage03.png

As the height from the weights to the floor is controlled to be constant, and the friction is kept constant by using the same runway, I expect Fweight will be proportional to d.

Method:

Apparatus List

Margarine tub

Masses

Long lab table as runway

Long sting

Rulers

Pencil

  1. Set up the apparatus as shown in diagram 1 in the introduction.
  2. Add weights into margarine tub and fasten them tightly. Record the total mass and keep this mass constant throughout the experiment.
  3. Hang 100g (150g, 200g, and 250g) weights on string. (The mass here is the independent variable. And because image01.png, I can then get the magnitude of the propelling force)
  4. Drop the weights from the constant height every time to propel the weighted margarine tub.
  5. Record the total forward distance (image04.png) by the tub. (image05.png, this is how I get the dependent variable)

Controlling the controlled variables:

  • The total mass of the weighted margarine tub is kept constant throughout the experiment by adding constant weights in it.
  • The friction of the runway is kept constant by using the same runway throughout the experiment.
  • The height from the hanging weights to the floor is kept constant by recording the height and dropping weights from this height every time.
...read more.

Middle

0.64

0.64

0.15000

0.87

0.87

0.85

0.86

0.20000

0.99

0.97

1.00

0.99

0.25000

1.09

1.11

1.11

1.10

* The mass of the weighted margarine tub is 0.166image06.png, and it is kept constant throughout the experiment.

* The height from hanging weights to the floor is 0.5image11.png, and it is kept constant throughout the experiment.

* The uncertainty in mass is estimated to be image12.png of the smallest division of the scale (0.0001kg)

image13.png

* The uncertainty in height is estimated to be image12.png of the smallest division of the ruler (0.001m)

image14.png

* The uncertainty in total distance is calculated fromimage15.png.

Sample calculation (experiment #1 when mass = 0.1kgimage16.png0.00005kg):

The uncertainty in distanceimage17.png

image18.png

image19.png

image20.png

* Sample calculation for average total distance (experiment #1 when mass = 0.1kgimage16.png0.00005kg):

image21.png

image22.png

image23.png

Processed Data Table:

Mass (kg)

Symbol: m

image24.png

Propelling force (N)

Symbol: Fweight

image25.png

Average distance (m)

Symbol: d

image08.png

0.10000

0.98

0.14

0.15000

1.47

0.36

0.20000

1.96

0.49

0.25000

2.45

0.60

* Sample calculation for force (experiment #1 when mass = 0.1kgimage16.png 0.00005kg):

image26.png

...read more.

Conclusion

I finished my experiment within the time limit (three classes). However, the range of values and the number of repetitions don’t seem enough for my graph. The reason for the limited range of values is that smaller propelling force can’t make the tub move, and the runway is not long enough for the weighted margarine tub to finish travelling under larger propelling force. I have done my experiment under the largest possible range.

Improvements:

To improve my results, I would try to avoid those uncertainties within my method as shown in diagram 1 that I have mentioned in evaluation. A way to do that is to install a fixed pulley at the corner of the lab table. The fixed pulley will reduce the amount of friction, and also keep the string parallel to the runway. By doing this, I can probably get more accurate results.

My results are also limited by my relatively small number of repetitions of my experiment. More repetitions can definitely make my result more accurate as they may give me a wider data to determine the uncertainties.

To make the uncertainties even less, I would like to choose a totally inelastic string to do the experiment because the stretch of the string may consume energy as well, therefore make the result less accurate.

...read more.

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