Question

A) During a lab, a meter stick was used at static equilibrium (the net torque was stationary and non-rotating objects are zero) to determine the masses or unknown distances for objects suspended from the meter stick. The total forces exerted at each location along the meter stick were factored in to find the total mass of the slotted masses, the mass hanger, and the clip that was attached to the meter stick. The one mass that did not have to be accounted for in the calculations was the mass of the clip that allowed the meter stick to sit on the pivot point. Why did the mass of the clip not included in the calculations? If the clip was made heavier would the system change at all?

B) If the meter stick was bowed, how would the bowedness effect the ability to calculate the torque accurately due to the force at a given position? What type of error would the bent meter stick produce in the experiment?

Answer 1

(A) In a meter stick experiment the net torque about the fulcrum is is equated to zero for considering the rotational equilibrium of the system (the stick ,the slotted masses, the mass hanger and the clip attached).

All the masses are placed at a certain distance from the fulcrum and they all contribute their part in rotating the system. Since the clip allowes the meter stick to sit on the pivot or the fulcrum. It's always placed where the pivot is. So it's perpendicular distance from the point or the axis of rotation (the pivot) is always considered to be zero. Hence Even if it has certain mass it does not provide any torque. That is the reason why the mass of the clip or precisely the torque due to its weight is not accounted for in the calculations.

Also there would not be any effect of the mass of the clip on the sytem even if it is increased or decreased provided the clip still remains a point object other wise if it would have certain dimensions then even a slight misplacement of the clip might produce error in the calculation of the net torque.

(B) If the meter stick is bowed then yes, it would definitely affect the calculations for torque. We know that torque produced due to any force depends on the perpendicular distance of any force from the point or axis of rotation. The bowedness of the meter stick would definitely decrease the perpendicular distance of the force due to gravity of different masses.

As a result of which the torque calculated for different forces due to the various masses will change which will result in errors.

This type of error would fall under the category of INSTRUMENTAL ERRORS under SYSTEMATIC MEASURMENT ERRORS. Since our instrument is defective due to which we are getting this error. As we would be taking the reading on the meter scale , but the actual perpendicular distance won't be as measured on the meter scale it would be somewhat less than the observed reading as the magnitude of cosine of the angle with which it bowed will be less than 1. Hence l' < l.

Where l' is the actual perpendicular distance. And

l is the measured distance on the meter stick.