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$2$ Force Question

Objective: To calculate the value of the acceleration due to gravity, g$,$ using new data col$-$ lected using a Force Table.

Given information:

Force $1$ located at $0$ degrees

Force $2$ located at $270$ degrees $($as marked on the board$)$

Force $3$ located first at $250$ degrees, then at $225$ degrees, then at $200$ degrees $($as marked

on the board$)$

$$ Standard error in the mean $=$n

The magnitude of Force $1,$ of Force $2,$ and of Force $3$ will be provided at the lab station.

Apparatus available:

$$ Force Table

$$ Strings $(4)$ with ring $$ Masses and hangers

Method: Do not move Force $1$ or Force $2.$ Put Force $3$ at $250$ degrees $($as measured on the scale on the board$).$ Place a fourth mass hanger with sufficient mass $($call this mass $4)$ at a position angle such that the system is in equilibrium. $($Assume that the numbers stamped on the masses are correct. Do not measure the masses$).$ Do this twice more, placing Force $3$ as described above in the given information, and adjusting mass $4$ and its position as required to achieve equilibrium. Compute a value for g for each trial, using both x and y coordinate information. In your analysis, use the standard convention for defining angles in a Cartesian coordinate system. Compute the mean g$,$ sample standard deviation, and the standard error in the mean. Define and label all terms used in your data and analysis. Show all work.