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Problem - a very large packing case, far too heavy to lift, and I want to drag it along the floor by a piece of rope. I am going to find the best angle at which i should pull the rope to reduce the drag of the box.

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Mechanics 2


Work where Modelling and Experiment are evenly Match

Written by Jian Qin Lu

  • Introduction

There is a very large packing case, far too heavy to lift, and I want to drag it along the floor by a piece of rope. I want to find that how does the force I have to use vary with the angle that the rope makes with the horizontal. And also I want to find the angle which minimises the force required.

First I will work out the angle theoretically, in other words, I will make a model of this situation. Then I will do a simple experiment to find what the degree of the special angle is practically. Finally I would like to compare the experiment results with the prediction of the model.

  • Assumption

        As do an experiment, I cannot make the environment to be perfect and when I make the model, it is impossible for me to consider every factory in this case. Therefore I need make some assumptions.

  1. The string used in this experiment is light and inextensible.

The rope used in this particular experiment is thin and about 1.5m long. So for this experiment, the mass of the rope is extremely small and it can be ignored. The string itself will extend when there are several forces acting on it. Hence it will create a tension on the string. However it is very small as well. Therefore I will ignore it when I model the experiment.

...read more.


  • The experiment

        Here is a list for the apparatus will be used in this experiment.

  1. a wood block
  2. a pulley
  3. a string
  4. a table
  5. a stand
  6. a rule
  7. an electronic scale

8. some weights

The diagram on the next page shows how this experiment works.


First I measured the mass of the block by using the electronic scale. And the mass of the block is 356g that is 0.356kg.

Then I made the sinA equal 0 that means the height from the top of the block to the pulley is zero, and the degree of angle A is zero as well. The reason why I use sin not the degree is it is very hard the measure degree when I did the experiment. And I cannot get an exactly degree of an angle. As compare with using degree, sin is more accurate. When the block is equilibrium, if A is zero degree, the tension on the string is the same as the friction force between the block and the table. So the friction force is the same as the weight of the weights. Then I can use the equation F=μR to calculate the coefficient of friction μ.

At this situation the weight of the weights is 92.56g (to 2 decimal place). Through calculation, the coefficient of friction μ is 0.26 (to 2 decimal place).

        As I know theμ, I can give the exactly value of the angle which minimises the force required theoretically. tanA=0.26 so A=14.57º

        The graph below shows the theoretical curve.


Then I have tried several angles by changing sinA.

...read more.


  • Revision of the process

        The other reason why these two results are difference is the assumption I made at the beginning. There are some factors I did not consider when I manipulate the model and did the experiment. The biggest two errors I think are the friction between string and pulley and the extension of the string.

        Since the friction between string and pulley dos exist, I need heaver weights to move the block. The reason is I need create extra force to cancel the friction. The extension of the string also required the bigger tension, because the extension of the string itself produced the extra resistant force.

        In order to improve this experiment, I consider the easiest point is that make the measurements more accurate. I can use a better rule to take the distance measurement, and use a more sensitive scale. Also I can improve the environment of the experiment to reduce the effect to the weight measurement.

        In order to improve the model, I think the best thing to do is considering more factors than I did in this course. For example, if I did not assume the pulley is smooth, the theoretical result should be more close to the real one, because the pulley does not smooth in practice. And I can consider the extension of the string as well. However that will make the calculation much more complicated than I have done in this coursework. If the mentioned calculations have been done, I can avoid these two biggest factors which make the prediction imprecise, and the prediction should be much better.

...read more.

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