Describe how a student could perform a laboratory experiment to determine the force constant of the elastic cord used in a launcher by plotting an appropriate graph. State the measurements to be taken and how they are used to find the force constant.
A conservation drone uses a slingshot-style seed-pod launcher to sow seeds across a valley. The launcher consists of an elastic cord secured between two horizontal support pins, as illustrated below.
The unstretched length of the cord is exactly equal to the 16 cm distance between the support pins. The midpoint of the cord is pulled back horizontally by a setback distance ddd.
The cord has a force constant of 800 N m-1.
The variation of the extension of the cord with setback distance d d\,d is shown in the graph above.
A seed-pod of mass 50 g is placed at the center of the cord and pulled back to d=6 cmd = 6\text{ cm}d=6 cm. The drone launches the seed-pod horizontally from a height of 3.6 m above horizontal ground.
Use the graph to show that the elastic potential energy E E\,E stored in the cord is about 0.64 J.
Show that the maximum speed at which the seed-pod leaves the launcher is about 5.1 m s-1.
Calculate the horizontal distance R R\,R travelled by the seed-pod before it strikes the ground. Ignore air resistance in your calculation.
Explain how the actual horizontal distance travelled by the seed-pod compares with the value of R R\,R calculated in (iii).
