Review linear relationships in Edexcel A-Level Physics through y = mx + c comparisons, graph validity checks and constant-gradient arguments.
A student investigated the bending of a plastic beam.
The beam, of width w and height h, was supported at either end by two metal rods a distance l apart, as shown.
She applied a force F to the middle of the plastic beam by hanging a mass from it.
The beam bent downwards as shown.
She measured the vertical distance d moved by the middle of the plastic beam and repeated this measurement for increasing values of F.
She recorded her results in a table, as shown.
The “bending modulus” E of the plastic beam can be calculated using the equation
E = l^3F/(4wh^3d)
Show that the gradient of the graph is equal to l^3/(4wh^3E).