Question

Objective: In this lab the Centripetal force required to maintain an object in uniform circular motion will be measured. The relationship between a rotating object's mass, velocity, and distance from the center of rotation to the centripetal force will be tested against theoretical expectations. Equipment: Centripetal Force Apparatus with 1, 2, 4oz weights, Force sensor, Magnetic field sensor, Short lab stand with cross bar, 500 g&1kg counter weights, scissors jack, "C" clamp Background: When an object is in uniform circular motion its speed (v), period (T), and distance from the center (R), are related as follows: v = 2 pi R/T Equation (1) The required centripetal force for a circling object is given below: F_c = mv^2/R Eq. (2a) or equivalent: F_c = (4 pi^2 mR)/T^2 Eq. (2b) In this lab you will be making plots of centripetal force on the Y axis and 1/T^2 on the X axis (see equation 2b.). From this graph you can readily check to see if your data agrees with theory. Explain why it is better to plot 1/T^2 on the X axis instead of simply T.

Answer 1

Given that, v = 2 pi R/T F = m v^2/R = m (2 pi R/T)^2/R = 4 pi^2 m R/T^2 F = 4 pi^2 m R/T^2 here since the object is in uniform circular motion, speed is constant also from above eqn, m, R are also constants for the object. When the time taken to complete on rotation changes (T) changes, the centripetal force also changes from above expression it is clear that as the T changes F also changes here the quantity, F depends on T so T is independent variable and F is dependent. Generally while plotting a graph always the independent variable should be taken on X - axis and dependent variable is taken on Y axis so 1/T^2 is taken on X - axis instead of an the Y - axis.