1. Torque in the Body Elizabeth Gjini Jack Jordan

2. Introduction Torque is the tendency of a force to cause or change rotational motion of a body. This is represented by the equation Ƭ=(F)(LA) where F is the force and LA is the length of the lever arm. When a force is applied closer to the fulcrum point, it will produce a smaller torque. When the force is applied at a larger distance from the fulcrum point a larger torque is produced. The human body’s muscles supply the force to rotate limbs about a point of axis in the joint. For muscles to produce a large torque they must supply a large force because the force is applied close to the fulcrum point. These large forces can cause pain and breakdown of the body’s joints, but the tradeoff is speed. This increases the body’s range of motion. This lab will explore how torque is applied in the body, specifically the arm.

3. Materials Balance Ruler Weights Rubber band LoggerPro

4. Experimental Procedure Place a ruler on the fulcrum point. Find the spring constant of the rubber band by measuring its length when it’s not stretched, adding a weight, and re- measuring the length while it is stretched. Plug the values into the equations K= mg/Δx and F= kx. Attach weights on either side of the ruler as well as the rubber band at a fixed point. Change the amount of weight or the distance on each side so that there is an equilibrium. Measure the distance of the weights from the fulcrum point. Place the recorded data into the equation T=F(LA) and plot the calculated data on LoggerPro.

5. Experimental Setup Fulcrum Point (acting as the elbow) Rubber Band (acting as the triceps) Weight (acting as the bicep) Ruler (acting as the arm)

6. Raw Data Measures Data m=.15kg Δx=.0275m Arm length total: 17cm + 13cm= 30cm Length rubber band stretched = 7cm Calculated Data K= mg/Δx = 53.45 (N/m) F= kx = 3.7415N

7. Observations A weight is placed at the end (where the hand would be) and the arm rotates when the same amount of force is applied. In order for the arm to stay level more weight must be added to the left side (the bicep must apply more force).

8. Raw Data Distance to the left from fulcrum point (cm) Distance to the right from fulcrum point (cm) Mass on the left (g) Mass on the right (g) 130 35050 2302031050 3301027050 TrialsAdded Weight (g)Distance (m)Torque (Nm) 13100.13.39494 23200.125.392 33400.115.38318 43600.11.38808 Part 2 Part 1

9. Comparison 270g 50g 30cm 10cm 350g

10. Data Analysis This graph shows how when distance on the right increases the weight on the left needed to balance the apparatus also increases.

11. Data Analysis In this graph distance is compared to torque. Torque will stay the same when distance on the right is decreased and weight on the left is increased. Distance v. Torque

12. Data Analysis Torque is equal to force*distance of the lever arm. This graph also shows that torque will stay the same when distance on the right is decreased and weight on the left is increased.

13. Analysis Cont. Different animals need different characteristics in order to be efficient. The human body sacrifices strength for speed while animals like the sloth sacrifices speed for strength. The sloth has weak muscles (low force) and long arms (large length) which generates high torque. This is seen in the equation Ƭ=(F)(LA). This allows them to hang on trees for extremely long periods of time without being noticed by predators. However, sloths have a small amount of muscle tissue. It takes large amounts of energy to move; sloths only move a maximum speed of 13 ft. per minute.

14. Analysis Cont. On the other hand, animals like the hummingbird can move their wings at high speeds. Their small wings (small length), but strong muscles (high force) produce a large torque [Ƭ=(F)(LA)]. This helps the hummingbird flap their wings at an average of 20-30 beats per second, or 1200-1800 beats a minute. The high torque in their wings lets them generate more lift and less drag allowing them to hover above flowers.

15. Conclusion We have explored the different aspects of torque, and in particular the application of torque in an organism. We showed that distance and force contribute equally to the magnitude of torque. We did this by showing that there is an indirect, linear relationship between different distances and forces that multiply to the same torque. We also explored how the manipulation of the relationship between distance and force is present in living organisms. Like how in a sloth a high distance between the force applied and fulcrum point is beneficial. This is because the sloth needs a lot of strength to hold its body weight on trees and branches. The high distance requires less force applied to achieve high amounts of torque enabling the sloth to easily hold itself up for extended periods of time. On the flip side, however, the high distance renders a slower moving arm. For an animal like the hummingbird a low distance between force applied and the fulcrum point is more beneficial. This is because the small distance enables the hummingbird to move its wings at ridiculously fast speeds. The small distance also means more force is required, but due to the light weight design of a bird’s wing this is not a problem. There was no surprising data. The slight discrepancies are due to human error.