Question

In an experiment to determine the spring constant of an elastic cord of length 0.60 m, a student hangs the cord from a rod as represented and then attaches a variety of weights to the cord. For each weight, the student allows the weight to hang in equilibrium and then measures the entire length of the cord. The data are recorded in the table below:

(a) Use the data to plot a graph of weight versus length on the axes below. Sketch a best-fit straight line through the data.

(b) Use the best-fit line you sketched in part (a) to determine an experimental value for the spring constant k of the cord.

The student now attaches an object of unknown mass m to the cord and holds the object adjacent to the point at which the top of the cord is tied to the rod, as shown. When the object is released from rest, it falls 1.5 m before stopping and turning around. Assume that air resistance is negligible. 

(c) Calculate the value of the unknown mass m of the object. 

(d) i. Determine the magnitude of the force in the cord when the when the mass reaches the equilibrium position. 

ii. Determine the amount the cord has stretched when the mass reaches the equilibrium position.

Answer 1

(b) The slope of the line is F/∆x which is the spring constant. Slope = 24N/m

(c) Apply energy conservation. U_top = U_sp(bottom).

Note that the spring stretch is the final distance – the initial length of the spring. 1.5 – 0.6 = 0.90 m