Question

Please help me make graphs with the data points provided and help me complete the analysis part of the the lab.

Answer 1

Part a) Springs

For the first part, the instructions say that you should plot the force on the spring versus the extension. From Hooke's Law, we know that:

`F=kx`

Where F is the force applied by a spring with constant k that is extended a distance x from its equilibrium position.

To find the force applied by the spring, multiply the hanging mass by the acceleration of gravity. Create a table showing force vs. extension. Using the vertical axis for the force F, plot the force on the spring versus the extension. Next, draw a straight line that describes the data points and calculate its slope.

For the second part, create a table where a column for the square root of the mass is included and plot the period versus the square root of the mass. We know that:

`T=(2\pi)/(√(k))√(m)`

The slope of the period vs. square root of mass corresponds to the factor 2π/√k, from which the constant k can be calculated.

Part b) Pendulum

First, create a table with a column where you calculate the square root of the length. Use the data from that column as the x-axis on your period vs square root of length graph. For a pendulum, we know that:

`T=(2\pi)/(√(g))√(l)`

From which we can identify that the slope corresponds to the factor2π/√g, from which the value of g can be calculated.