A student devised an interesting experiment to measure the repulsive between two bar magnets. She used an incline with a very low coefficient of friction, placed one magnet at the bottom of the incline, and let the other magnet find its equilibrium position with respect to the fixed bottom magnet. The setup is shown above. She varied the angle θ, measured the separation distance x between the two north poles of the magnets, and obtained the following data.

sinθ 0.05 0.10 0.15 0.20 0.25 0.30
x (cm) 14.10 9.80 8.20 7.00 6.40 5.60

Show that the equation relating the magnetic force kxn to the component of the moveable magnet’s
component of weight along the incline is mg sin θ = kxn, where m = 0.05 kg is the mass of each
magnet, k is a constant, and g = 9.8 m/s2 is the acceleration due to gravity. (b) Plot a straight-line
graph of the appropriate variables, and from the slope and intercept of the graph, determine values for n
and k.

Question

A student devised an interesting experiment to measure the repulsive between two bar magnets. She used an incline with a very low coefficient of friction, placed one magnet at the bottom of the incline, and let the other magnet find its equilibrium position with respect to the fixed bottom magnet. The setup is shown above. She varied the angle θ, measured the separation distance x between the two north poles of the magnets, and obtained the following data.

sinθ    0.05 0.10 0.15 0.20 0.25 0.30 
x (cm) 14.10 9.80 8.20 7.00 6.40 5.60

Show that the equation relating the magnetic force kxn to the component of the moveable magnet’s
component of weight along the incline is mg sin θ = kxn, where m = 0.05 kg is the mass of each
magnet, k is a constant, and g = 9.8 m/s2 is the acceleration due to gravity. (b) Plot a straight-line
graph of the appropriate variables, and from the slope and intercept of the graph, determine values for n
and k.