Physics Lab 7

Physics 2021 Group: Kaya Brown and Amelia Maughan Lab 7: Statics in The Human Body Goals An anticipated goal of this experiment is to comprehend the criteria for achieving static equilibrium in the presence of concurrent forces and torques. Another goal is to demonstrate the applicability of basic lever models in representing anatomical joints within the human body. Students should also be able to establish relationships that elucidate the mechanical advantages and disadvantages associated with different types of levers. Procedure A meter stick centered on a fulcrum to hold a weighted force and muscle force located at equal distance on the opposite end by hangers in experiment one. 350 grams of weight is placed on the hanger at one end as the force sensor is attached to the opposite end. The applied force is measured in capstone as the sensor is pulled down until the meter stick is level, indicating static equilibrium. In experiment two, the weight of 800 g is placed a few centimeters from the fulcrum as the force sensor is lifted at the same end further from the weight. The force value is measured and recorded. In experiment three, the force sensor and weight switch positions on the same side, which proves to be difficult to lift. This experiment represents the bicep when it is flexing to lift the forearm, so the meter stick must be gently held down near the fulcrum while the force is recorded.

Error and Precautions A possible source of error could include a non-uniformly distributed mass of the meter stick. This error could potentially cause larger force required if the distance were smaller, or less force if the imbalanced distance were closer to the fulcrum. Another possible source of error could be failing to lift or pull the force sensor to a level of static equilibrium. Pulling too far down/up will produce a higher value of force required in N and will not net to zero. Results Figure 1.1 Predicted values versus actual values of force in newtons Experiment Predicted force (N) Actual force (N) 1 4.00 3.82 2 2.00 2.61 3 10.10 13.19 Percent error exp 1: %E = |3.82-4.00/4.00| *100 = 4.5% Percent error exp 2: %E= |2.61-2.00/2.00| *100 = 30% Questions Question 1. When the head is in static equilibrium, how does the torque produced by the muscle compare to the torque produced by the weight of the head? Use your answer to make a

input force and the output force on the load. Also, to simplify we can assume the forces are perpendicular to the lever arm. Fd 2 - wd 1 = 0 Fd 2 = wd 1 (2.00 N)*(24.0 cm) - (.800 kg*10 m/s^2)*(6.0 cm) = 0 Question 4. Mechanical advantage comes at a cost. Use trigonometry to show that, as the wheelbarrow is lifted,the vertical distance the load moves is less than the vertical distance the handles move. Hint: you will need to use either the tangent formula or the arc length formula. Be sure to include a diagram. F = tanθ F = (y 1 /d 1 ) = (y 2 /d 2 ) = y 1 > y 2 (d 1 /d 2 ) y 2 < y 1

Question 5. In static equilibrium the forces balance as well as the torques. Use force equilibrium (net force equals zero) to find the force on your fulcrum, a.k.a. the downward force on the elbow joint, a.k.a. the force your finger provided. To do this, use your known values for the weight and muscle force to find the unknown value. F = tanθ F = (y 1 /d 1 ) = (y 2 /d 2 ) = y 1 > y 2 (d 1 /d 2 ) y 1 > (0.800 kg*10 m/s^2)*(6.0 cm/24.0 cm) y 1 > 2.00 13.19 > 2.00 Question 6. Show using the torque equilibrium condition why very large forces must be generated by the bicep to lift even a small weight. Be sure to accompany your proof with a short explanation. F muscle > F weight F weight = mg*d 2 F muscle = mg*d 1 mg > mg*(d 1 /d 2 ) mg*(d 1 /d 2 ) < 1 Because d 2 is much greater than d 1 , then d 1 /d 2 is much smaller than 1. Therefore, F (the forces generated by the bicep/muscle) is much larger than mg (the weight of the object being lifted). The length of the lever arm from the elbow to the weight plays a crucial role in

Discussion In part one of the the experiment, the predicted muscle force needed to maintain static Equilibrium was 4.00 N. In a human head, 𝑟 muscle and 𝑟 weight are approximately equal, the equation was set equal to zero. The value obtained from the experiment was 3.82 N, giving a 4.5% error. When the center of mass became shifted, distance of 𝑟 weight was increased by 13.25 cm and measured by the force sensor to be 5.86 N. Using the foot as an example of a class II lever, the force value predicted from the muscle force position on the same side of the weight at 800 g that must be provided to hold the meterstick horizontal in static equilibrium was 2.00 N. The calculated force given by the experiment was 2.61, with a 30% error. In experiment 3, muscle force calculated from the replicated action of a bicep lifting 300 g was 13.65 g. This value is reasonable because more energy must be applied to displace the weight to a longer distance.