Physics » Vectors and Scalars » Components Of Vectors

Force Board Experiment

Let’s describe an experiment on using force boards to determine the resultant of vectors. In this experiment, we use a force board to determine the resultant of three non-linear vectors. If you are interested in carrying it out, you will need blank paper, force board, 4 spring balances, an assortment of weights, gut or string and four pulleys per group. One should be able to get these in a functional school physics laboratory.

The experiment should provide you with the opportunity for you to see an abstract mathematical idea in action. You can use graphical techniques such as the tail-to-head method to find the resultant of three of the four measured forces. The questions at the end of the experiment should guide you in thinking about the results you have obtained.

Informal Experiment: Force Board

Aim

Determine the resultant of three non-linear forces using a force board.

Apparatus and materials

You will need:

  • blank paper
  • force board
  • 4 spring balances
  • assortment of weights
  • gut or string
  • four pulleys

Method

Before beginning the detailed method think about the strategy. By connecting a cord to the ring, running it over a pulley and hanging weights off it you can get a force exerted on the ring. The more weights or heavier the weight you hang the greater the force. The force is in the direction of the cord. If you run a number of cords over pulleys you are exerting more forces, all in different directions, on the ring. So we have a system where we can change the magnitude and direction of the forces acting on the ring. By putting a spring balance between the cord and the ring, we can measure the force. Putting a piece of paper under the ring allows us to draw the directions and the readings on the spring balances allows us to measure the magnitude.

We are going to use this information to measure the forces acting on the rings and then we can determine the resultants graphically.

  1. Set up the forceboard and place a piece of paper under the ring.

  2. Set up four different forces by connecting a spring balance to the ring on the one side and some cord on the other side. Run the cord over a pulley and attach some weights to it. Work in a group to do this effectively.

  3. Draw a line along each cord being careful not to move any of them.
  4. Make a note of the reading on each spring balance.
  5. Now remove the paper.
  6. Working on the paper, draw each line back towards the where the centre of the ring had been. The lines should all intersect at a point. Make this point the centre of your Cartesian coordinate system.
  7. Now choose an appropriate scale to relate the length of arrows to the readings on the spring balances. Using the appropriate spring balance and correct line on the paper, draw an arrow to represent each of the forces.

Results

For two different choices of 3 of the force vectors we will determine the resultant. To determine the resultant we need to add the vectors together. The easiest way to do this is to replicate the vectors using a ruler and protractor and draw them tail-to-head.

Conclusions and questions

Note the direction and the magnitudes of the resultants of the various combinations.

  1. How does the calculated resultant compare to the vector that wasn’t used to calculate the resultant in each case?
  2. What general relationship should exist between the resultant and the fourth vector and why do you think this is the case?
  3. Would this be the same if we had more or less forces in the problem? Justify your answer.

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