Question

V. Questions Discuss how and why the following physical quantities would or would not affect your measurements and their possible relative contribution of errors to your measurements. Als 1. 2. 3. o, comment on how you would try to minimize those errors and correct for them. friction in the pulleys finite mass of the pulleys forces due to the strings are not perpendicular to the tangent to the ring at that point 4. dificul to udge whether the ringis perféctlyhorizontal the ring and all the threads are not in the same plane the force table is not perfectly horizontal 5. 6.

Answer 1

1. Due to friction extra tension is added. Thus, the tension in the string differs from its tension value in case of ideal pulleys. This leads to a variation in the measured results and calculated ones (considering ideal frictionless pulleys). The error due to friction can be minimized by using low friction ball bearing pulleys or by arranging the pulleys in a manner such that the net tension due to all the string at a common point reduces to zero (polygon of forces).

2. If the pulleys have finite mass, they will have a finite moment of inertia which will affect the measurement values. The tension along string on both sides of the pulley is taken as same assuming that the pulley is massless. When a pulley of finite mass is rotating it will have an unbalanced torque in the direction of rotation. Thus, the tension along the string on both sides of the pulley will not be same. So, while calculating if the moment of inertia of the pulleys are ignored in the equation of forces, the measured values will differ from the calculated values and hence leads to error. This error can be minimized by using light pulleys of smaller radius. It can be reduced by modifying the experimental setup such that it comprises of pulleys with same mass, rotating at a same angular speed in opposite sense so that the net torque due to their finite moment of inertia adds up to zero or to a minimum value.

3. If the forces due to the strings are not perpendicular to the tangent to the ring at that point, then the Normal force of the pulley on the string will have a component along the tangent to the ring along which the string experiences tension. As such, the tension values changes and will differ from the values used in calculations. This will differ the measured values of the pulley experiments with the calculated values. The error in measurements can be reduced by polishing the groove on the pulley through which the string passes.

4. Here the ring is not defined in the question. We assume the ring to be the pulley. If the ring/ pulley is not perfectly horizontal then there appears extra friction when it rotates about a fixed axle. This frictional force will introduce error in measurements. In order to minimize error, the horizontal allignment of the ring can be ascertained with the help of a spirit level and alligned accordingly along the horizontal.

5. If the ring and all the threads are not in the same plane then there will be a torque acting on the strings threads which will vibrate the ring in the vertical plane. In order to minimize error, the ring and all the threads should be alligned along the same plane.

6. If the force table is not perfectly horizontal, then the vertical components of the forces involved in the experiment won't be zero and this will effect the measured values. In order to minimize the error the force table should be perfectly alligned along the horizontal with the help of leveling screws.