Equilibrium of a Rigid Body PDF

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Equilibrium of a Rigid Body

Name: Chel, May Myet Partner’s name: Melissa Finnegan PHY 116 – 13725 Lab number 11 – Equilibrium of a rigid body Date: 11/21/2017 Instructor’s name: Mihaela Drenscko

Objective: The purpose of this experiment is to study the conditions that must be satisfied for a rigid object to be in static equilibrium and to measure the torques acting on a rigid body and to determine the conditions necessary for equilibrium to occur. This is done by computing the total torque acting on a meter stick by means of weights suspended at specific locations on the ruler. Principles/laws tested and used: When a force is applied to a rigid body at any point away from its center of rotation, the force will have the tendency to cause clockwise or anticlockwise rotation. Such a force is described as Torque (τ), which is a product of the radius (distance from rotation point), the magnitude of the force and sin(θ), where θ is the angle at which the force is applied. Therefore, τ = r F sinθ. When an object is at equilibrium the sum of the sum of the forces applied is equal to zero, therefore, the torque applied to the left of the pivot point must be equal to the torque applied to the right of the pivot point. The torque τ exerted by a force F on a rigid object able to rotate about an axis is given as τ = F d, where d is the lever or moment arm of F about axis. It is equal to the perpendicular distance from axis to F. Torque is a vector quantity that is perpendicular to the plane made by F and d. For rigid bodies in equilibrium, they should not have neither linear nor angular acceleration. This means that two conditions must be satisfied simultaneously; the total force acting on the object is zero and the total torque should also be zero. Hence Στ=0 and

ΣF=0

By convention, the torque is positive if the force tends to rotate the object counterclockwise and negative if it ends to rotate clockwise. The apparatus consists of a meter stick balanced about a pivot. The torques are created by weights hung at different locations along the ruler by means of clamps. Discussion and Errors: In this experiment, all forces acting on the ruler will be perpendicular to it and θ = 90˚. Since, Sin 90˚ = 1, therefore, the torque acting on the meter stick will be a product of the magnitude of the force and the radius. In this experiment, we will use the relationship between opposing torques at equilibrium to determine the radius, mass or pivot point within an equilibrium system. Since the forces acting on the meter stick are all at 90˚ to the stick, sin 90 will be 1. Therefore, we can conclude that torque will be a product of the magnitude of the force and the radius. The magnitude of the force is weight, which is the product of the object’s mass and acceleration due to gravity. Torque can then be represented as the product of the objects mass, acceleration due to gravity and or distance from the turning point (τ = m × g × r). Along with the fact that opposing torques are equal for a body at equilibrium, we can calculate the expected mass or radius of an object given that the opposing mass and radius are known. We may also determine the position of a new pivot point away from the center of mass of the meter stick by adding the contributing torque from the mass of the stick which acts at its center of gravity. The theoretical mass, radius and pivot point were calculated and compared to the experimental values which were observed during the experiment t. All values were relatively close with the percentage difference being recorded at 0.75%. This difference may have been caused by errors which occurred during the experiment. Errors such as systematic errors associated with the instruments used or gross errors which occurred while reading the instruments. A swinging mass may have also caused errors when determining the pivot points. Conclusion: The torque acting on a rigid body could be determined along with the conditions (mass and radius) required for equilibrium by applying the fact that opposing torques acting on a body at equilibrium are equal.

Apparatus:        

Meter stick One knife-edge meter stick clamp without clips Two knife-edge meter stick with clamps Two 50g hangers Slotted weights Meter stick support stand Large friction box Electronic balance

 Diagram of Apparatus 

Computations and Questions:

Sin 90˚ = 1 g = 9.8m/s Computations are in the data sheet. Percentage Error: ¿ Theoretical value−Experimantal value∨ ¿ Percentage Difference:

¿ Value 1−Value 2∨

¿ × 100 (Value1+Value 2)/2 ¿

¿ × 100 Theoretical Value

Questions: 1) length of meter stick = 1 m place mass of 5 kg at x m balance torque at the center m1g * 0.5m = m2g * x 3*0.5 = 5x x = 0.3 m (0.5 + 0.3) = 0.8 m from the left end 2) It will fall on the side with the greater torque. 3) Yes, we can apply the equation. But, the net force will not be zero in this case. Net torque about center = Angular acceleration * movement of inertia of stick about balance point....