Physics Exp 8 lab report 10-29

Equilibrium Exp. 8: Equilibrium Using Model of Human Arm Hailey Abell William Wagner Physics 1100L Lab 2 November 2023 ABSTRACT An experiment was performed that involved motion, torque, equilibrium, and force. When Newton’s Law is applied to translational motion, constant linear acceleration requires no linear acceleration and has no force acting on it. Rotational motion does not involve rotational acceleration and has no torque acting on it.

INTRODUCTION A body is in a state of equilibrium when it has a constant linear velocity and a constant rotational velocity. Equilibrium can have situations of uniform motion and no motion. It is known that the result of all forces acting on an object must be zero. The result of all torques around an axis must also be zero. The weight of a mass can be determined using F = mg , which is also the force. The magnitude of the torque is determined using the equation: τ = X F ⊥ , where X is the moment arm or the distance from the spin axis to the applied force. In this experiment, an apparatus that had a similar structure to a human arm was used. The equation for the equilibrium of the vertical forces is ∑ F = F b cosθ − F h − F f − F e = 0 , where F b = force of bicep, F h = force of hand, F f = force of forearm, and F e = force of elbow. The equation for equilibrium of the torques is: ∑ τ = ¿ τ h + τ f – τ b = 0. To determine F e , use the equation: F e = F b cosθ − F h − F f . The equation for F b is shown below where τ h is the torque of the hand and τ f is the torque of the forearm. F b = τ h + τ f ( X b )( cosθ )

Part 1-e of the experiment was like the previous steps but involved a 100-gram weight on the hand. The “Bicep” force was determined using the equilibrium of torques and compared with the measured “Bicep” force. The final step, part two, of the experiment began by attaching the spring scale to the “Bicep” attachment point that is closest to the elbow. The 100-gram force was applied to the “Hand” to compare how the “Bicep” force changes with a different attachment point. RESULTS No weight on “Hand” Measured F b from 1-a F b = 1.4 N % Difference 1.59% Calculated F b from 1-b F b = -1.42768 N 50-gram weight on “Hand” Measured F b from 1-c F b = 2.8 N 3.00% Calculated F b from 1-d F b = -1.99315N 100-gram weight on “Hand” Measured F b from 1-e F b = 4.2 N 3.90% Calculated F b from 1-f

F b = -3.71577 QUESTIONS/DISCUSSION: 1. Comment on how well the measured “Bicep” force compares to the calculated “Bicep” force for each of “no weight”, “50-gram weight”, and “100-gram weight”. Include the % difference values for each in your comment. Is there one set that agrees better than the other sets? When no weight was added to the hand, the smallest difference between the measured values and the calculated seemed to occur. The difference increased as the weight increased. The percent difference of the hand with no added weight was the smallest at 1.59%. The percent difference of the hand with a 50-gram added weight came out to be 3.00%, and the percent difference of the hand with the 100- gram weight was the largest with a percent difference of 3.90%. The hand with no added weight agreed better than the other sets did. 2. Whenever you measure various quantities in an experiment there are uncertainties associated with these measurements. Refer to the uncertainty analysis instructions found online on Pilot to state which measurements of this experiment are considered systematic, and which are considered random. In your statement give reasons why they are systematic, and why they are random. The measurements of X b , X b , and X h are considered random, this is because, when measuring, the line of the ruler lands between two measurements, not directly on a measurement line. The weights are a source of systematic uncertainty because, the scale repeatedly gave the same value for an object, and then gave a different value when nothing else changed. 3. In part 2 you changed the attachment point at which the “Bicep” is attached to the forearm. Compare the measured “Bicep” force from part 1-e to the measured “Bicep” force from part 2. Include both values in your answer. Discuss the reasons why there is a difference between the two values. When the bicep was attached to the point furthest from the “Elbow” in part 1-e the measured “Bicep” force was 4.2 Newtons When the attachment point changed, and the “Bicep” was attached to the point closest to the “Elbow” the measured “Bicep” force was 5.13 Newtons. This change in force is due to the shorter attachment point and the change in the angle.