Understanding Newton's First Law for Force Tables

[azn4lyf89]

I did an experiment on a force table with pulleys and weights. We were suppose to, through trial and error, find weights and add them on strings that were placed at different angles, so that the ring in the middle would become centered. Attached is the data table. I am suppose to calculate the algebraic sums of the x and y-components and see if Newton's First Law is verified within experimental error. I know that the sums should add up to zero, but am I suppose to put a negative value on the component that is opposite from the other? Should the X components add up to be zero and the Y components or together should they equal zero?

 

[tiny-tim]

I am suppose to calculate the algebraic sums of the x and y-components and see if Newton's First Law is verified within experimental error.
I know that the sums should add up to zero, but am I suppose to put a negative value on the component that is opposite from the other?
Should the X components add up to be zero and the Y components or together should they equal zero?

Hi azn4lyf89!

i] Yes … components in the negative direction are negative.

ii] This is vector addition … the vector sum must be zero, so the X components and the Y components must equal zero separately.

 

[baba89]

First of all, great job conducting an experiment to verify Newton's First Law! It is important to test scientific principles through experimentation in order to confirm their validity.

To answer your question, yes, the algebraic sums of the x and y-components should add up to zero if Newton's First Law is verified. This is because the law states that an object will remain at rest or in uniform motion unless acted upon by an external force. In this case, the external force is the weight added on the strings, and the balanced forces in the x and y directions will result in the ring remaining centered.

In terms of assigning negative values to the opposite component, it depends on how you define your coordinate system. If you choose the positive x-direction to be towards the right and the positive y-direction to be upwards, then the opposite components would have negative values. However, if you choose the positive x-direction to be towards the left and the positive y-direction to be downwards, then the opposite components would have positive values. It is important to be consistent with your coordinate system throughout the experiment and calculations.

In conclusion, if the algebraic sums of the x and y-components do add up to zero, then Newton's First Law is verified within experimental error. It is important to carefully analyze and interpret your data to draw accurate conclusions. Keep up the good work in your scientific investigations!