Sensors: Loggers: Force Any EASYSENSE Science in Sport Logging time: SnapShot with Asks for Value function Teacher s notes 401 Forces in levers Read Body movement is created by applying forces across joints in a rigid skeleton. The forces generated are altered by the effective levering created by the length of the bones either side of the joint and the position of the joint to the relative point of movement. When considering the movement of limbs compared to a classic demonstration of levers the Lever - is nearly always the bone. Fulcrum is the pivot point of the lever, which is usually the joint Muscle Force is force that draws the opposite ends of the muscles together Resistive Force - force generated by a factor external to the body (e.g. gravity, friction etc.) that acts against muscle force Torque - the degree to which a force tends to rotate an object about a specified fulcrum Lever systems are classified according to the position of fulcrum, effort and resistive force. First Class levers: Force and resistive force are on opposite sides of the fulcrum. E.g. a see saw, scissors Example in physiology of a first class lever: Muscle force and resistive force are different sides of the fulcrum e.g. the head (cranium) resting on the vertebral column. As the head is raised, the facial portion of the skull is the resistance, the fulcrum is between the atlas and occipital bone, and the effort is the contraction of the muscles of the back. Second Class levers: Force and resistive force are on the same side of the fulcrum E.g. wheelbarrow, nutcracker Example in physiology of a second class lever: Muscle force and resistive force act on the same side of the fulcrum, with the muscle force acting through the lever longer than that through which the resistive force acts - e.g. raising the body up onto the toes. The body is the resistance, the ball of the foot is the fulcrum, and the effort is the contraction of the calf muscle. Third Class lever: Force and resistive force are on the same side of the fulcrum, but the force in is greater than the force out. The distance moved by the resistive load is greater than the distance moved by the force. E.g. broom, shovel, nail clippers. Example in physiology of a third class lever: Muscle force and resistive force act on the same side of the fulcrum, with the muscle force acting through the lever shorter than that through which the resistive force acts - e.g. adduction of the thigh. The weight of the thigh is the resistance, the hip joint is the fulcrum, and the contraction of the adductor muscle is the effort. T401-1
Most of the limbs of the human body are articulated by third class levers. A characteristic of third class levers is the increase in speed and a reduction of force. Human skeletal systems have evolved to give quick movement not strong forces. To work out the lever system in use in the body you need to be able to identify the fulcrum, muscle insertion point and the output of the movement relative to insertion point. This is not always as obvious as may be first believed. For example when you raise yourself up on your toes the fulcrum point is the ball of the foot, the insertion point is at the back of the heel and the resistive load is along the line of the leg bone. The fulcrum is not at the junction of the leg bone to the foot. An understanding of how levers affect movement and develop speed and power is important in sport, even if the full physics are not understood, the principle will help explain why some techniques are more productive that others. It can help in training for events such as javelin, tennis, hockey, boxing, etc. It can also help in aptitude selection for a sport. In this experiment, first class levers are studied they are simpler to understand. From the results, the mechanical advantage of the moments of the system can be calculated. The investigation could be introduced using small masses to create the balance and then use the Force sensor to measure the forces being created. The Force sensor allows the forces to measured at any distance along the balance, if the distance from fulcrum to sensor is measured the relationship between force x distance can be easily studied. Using the Force sensor and either pushing down or pulling on the sensor allows the students to feel the forces required to balance the track. Moving masses along the track to create the balance may give a mathematical solution, but it does not create an interaction between the balance and the size of the force. Experience also shows that creation of the balance point can be very time consuming and difficult to achieve, with quite a margin for errors. With the Force sensor, the forces are being measured at the point the sensor is located; graphing Force vs. Position will give a good straight line. Apparatus 1. An EASYSENSE logger. 2. A Smart Q Force Sensor with hook fitted. 3. The track from a Dynamics system. 4. A 500 g mass. 5. Blu-Tack or sticky / masking tape. 6. 2 small brackets from the Dynamics system. 7. 3 small hex bolts and wing nuts from the Dynamics system. 8. A small block (e.g. matchbox). 9. Rubber band. Set up of software and logger Use the setup file 401 Forces in levers. If you wish to set up the logger and software manually, Recording method Pre-log Function Pre-log Function name and unit SnapShot General, Asks for Value Distance (cm) T401-2
Notes Care should be taken to ensure the Force sensor is not overstressed. Refer to the sensor booklet prior to the experiment to check on use and limits of the sensor. The + and seen next to the force values are indication of the direction in which the force is being applied. For this work, the signs can be ignored. They have no mathematical significance. The apparatus lists a Data Harvest Dynamics system track as the balance beam; this is a long rigid aluminium beam and provides a very stable platform for the investigation. A metre stick is useful as the lever. It has distance measured on it, but any thin rod with low flexibility will do. A fulcrum is made using 2 x small brackets from the Dynamics system. A small block or box is needed to stop the brackets from moving together and a medium rubber band is used to hold them against the box, see the diagrams below for guidance. Alternatively a fulcrum can be made from 2.5 cm by 2.5 cm wood cut diagonally. A broom handle can also be used but it would need to be fixed to the bench with a piece of Blu Tack or similar. For the work outlined in this worksheet the fulcrum can be under the balance beam. If more accurate work on levers was required the fulcrum should be at the centre of gravity of the beam i.e. using the side slot of the balance beam. The Force sensor gives a more easily understood reading than using balanced forces. It can be used to either measure the force pushed down on the track or the force used to pull the track down to balance. To record the force when pulling down on the track you will need to slide a hex bolt into the side slot of the track (use the numbered side for convenience of distance measurements). The hook on the Force sensor can then be used to hook over the bolt. Pulling on the Force sensor will pull the track down and show the force being used. T401-3
The Force Sensor can also be used to push down on the runway directly. Remove the hook attachment and replace it with the larger black flat solid safety stop. Place the Force sensor on the track and use the tare to bring the force reading down to zero. Position the sensor at the correct distance and push down on it, the force required to balance the track will be shown. You may need to make allowance for the mass of the Force sensor; this is also producing a force. Sample results Data as collected. 500 g mass (nominal) at 40 cm from fulcrum. Force of masses = 4.6 N. A bar chart is used as the measurements are at fixed intervals. The students need to use the data at the sampling location they are not expected to interpolate or extrapolate the data. Force values multiplied by -1 to make positive force values (Tools, Post-log Function, General, Multiply by a constant). T401-4
Moments calculated using distance x force. (Tools, Post-log Function, General, Multiply channel by channel). Auto scale graph 0 to Max applied, original force data hidden. Experiment Distance of mass from fulcrum dr (m) Force produced by the mass, Fr (N) Moment of fixed mass dr x Fr (Nm) Force sensor distance, de (m) Measured force from sensor, Fe (N) Moment at Force sensor de x Fe (Nm) 1 0.4 4.6 1.84 0.4 4.4 1.76 2 0.4 4.6 1.84 0.3 6.2 1.86 3 0.4 4.6 1.84 0.2 9.5 1.9 4 0.4 4.6 1.84 0.1 18.9 1.89 Force of mass = mass in kg x 9.8. The mass used in the example had a nominal value of 500 g (5 x 100 g masses), checking with balance the mass was 0.468 kg. Depending of the aim of the lesson it may be T401-5
worth bringing this to the attention of the students and having a balance available to check the masses used. Moment of the fixed force compared to moving force shows a good match. As the fulcrum distance to Force sensor becomes larger, the mass of the sensor on the balance becomes more important. No allowance has been made for this in the above sample results. A difference of 2-3 mm from the measurement point can make the calculated moment vary, care needs to be taken when positioning the Force sensor. Using a larger fixed mass would reduce the error, but may become more difficult to fix to the apparatus. Unit d r F r d e F e Definition Distance from the fulcrum to the centre of the mass Force produced by the mass (mass x Newton correction) Distance from fulcrum to the centre of the force sensor attachment Force measured at sensor to balance the force of the mass At the end of the exercise it is hoped that students will begin to appreciate that brute strength alone is not enough to move faster or throw further. Some thinking is required to make the body and the apparatus of the sport work together. It should be obvious that a mass closer to the fulcrum requires more effort to move it over the same distance than if it was positioned further along the balance beam. T401-6