Lab 7 - kinetics

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APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 1 APA 2315 LAB 7 – KINETICS: FORCES AND MOMENTS OF FORCE Jeremiah Zephir 300130890 (Total: 50 Marks) OBJECTIVES: 1. To investigate Newton’s three laws of motion; 2. To understand the relationship between the variables associated with force; 3. To be able to draw a free body diagram (FBD); 4. To identify and calculate the forces and moments of force acting on a body; 5. To understand the concept of static equilibrium; 6. To evaluate various frictional situations and calculate the coefficient of static friction. INTRODUCTION: Sir Isaac Newton was a pioneer of mathematics and physics. In 1687, his seminal work Philosophiæ Naturalis Principia Mathematica (commonly known as Principia ) was published and has been called the single most influential book on physics (and possibly all of science!). Included in this fundamental work are his three laws of motion which have helped quantify and explain nearly every motion in the universe, from planetary orbits to everyday human movements. Each of the laws are stated below in their original form, translated to English. Newton’s first law : “ Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it .” (Newton, 1947, p.13) This means that a body will remain at rest (i.e. continue to be not moving) or in constant linear motion (i.e. moving in a straight line at a constant speed) unless acted upon by an external, unbalanced force (i.e. a resultant force that isn’t equal to zer o). When the resultant force acting on the body is zero, there is no change in the motion! Newton’s second law : “ The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed .” (Newton, 1947, p.13) This tells us that when a force (i.e. a push or a pull) is applied to a body, the body will respond with a change in motion (i.e. an acceleration) proportional to the force and in the same direction. This law also tells us that the resulting acceleration is inversely proportional to the mass of the body. The heavier the body, the less it will accelerate when pushed/pulled! This can be written mathematically as Ʃ F = m a . Newton’s third law : “ To every action there is always opposed an equal reaction .” (Newton, 1947, p.13) This explains that for every force, there must be a reaction force. The reaction force is always equal in magnitude to the action force but opposite in direction, and acts on a different body (e.g. ground, wall, chair, ball…).

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 2 As mentioned above, a force is a push or a pull. Muscles pull on bones to affect their motion. In soccer, when your foot (or head!) strikes a ball, the ball gets a push. When you collide with someone, the collision applies a push to both of you. It is important to remember that every force has the following characteristics: Magnitude: size (how big the push or pull is) Direction: which way the force is pushing or pulling Point of application: where the force is acting on the body Line of action: an imaginary extension of the force in both directions, which is useful in determining the turning effect of a force Force is a vector quantity . It is graphically represented by an arrow. Typically, a standard Cartesian coordinate system is used to represent the direction of a force, with the y-axis the vertical direction and the x-axis the horizontal direction. The positive directions are upward (vertical direction) or to the right (horizontal direction), and negative directions are downward (vertical direction) or to the left (horizontal direction). Force is measured in Newtons (N) . When a force is applied at an angle, the angle of application is provided relative to the right horizontal axis, or a specified reference line. When multiple forces act on a body, each force affects the body. When the contribution from the individual forces is added up, we are left with the net force. Net force is defined as the vector sum of all the external forces acting on an object. You can use the force components to find the resultant. In order to do this, you can use the Pythagorean Theorem and the arctan trigonometry function. You can also resolve a force into components. Remember SOH CAH TOA . Free Body Diagram (FBD) A free body diagram is used to simplify the analysis of a biomechanical problem. This kind of diagram isolates a particular body from all other bodies and the environment. It separates all action forces from their associated reactions, reducing the complexity of the analysis. Space diagram Free Body diagram +920 N +200 N +600 N 70

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 3 Rules for constructing a FBD Rule 1. Select the appropriate body or body segment , keeping in mind the unknowns you want to compute. That is, make sure the FBD includes at least one of the unknowns. Rule 2. Draw all known forces or moments of force at their respective points of application (e.g., weight vector, measured external forces, etc.). Note that the weight vector is placed at the center of gravity of the free-body. Rule 3. Draw all unknown forces and moments that directly contact the free-body. These include points of detachment from other parts of the body and points of contact with the environment. Wherever the free-body is separated from other parts of the body, replace the excluded parts of the body with an unknown force (two components) and a moment of force. Rule 4. DO NOT include internal forces which originate and terminate within the free-body (e.g., muscle joint forces of internal joints). Reminder: *** Statics is the field of applied mechanics concerned with the mechanical analysis of bodies at rest ( motionless bodies) . This state of “motion” is called static equilibrium . Statics is mainly used in the analysis of structures or the stability of bodies. In biomechanics, this includes the study of postural control, starting positions in sports, stresses in seated operators or the loading in manual material handling (lifting) tasks. Although statics only considers bodies that are motionless, the laws of statics apply equally well to bodies that are in constant linear motion. Static equilibrium is the state defined by Newton’s first law, whereby an object will remain in a state of rest or constant linear motion, unless acted upon by an external unbalanced force. When an object is in static equilibrium, the external forces acting on the object form a closed polygon with the resultant force equal to zero. For rigid bodies, the law must be extended to include that for static equilibrium the resultant moment of force acting on the body must also equal zero. This means that the rigid body must be rotationally motionless or spinning at a constant angular velocity whenever the sum of +

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APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 4 all external moments is zero. Mathematically, the static equilibrium of a rigid body occurs when both the following conditions hold: Ʃ𝑭 = 𝟎 Ʃ𝐹 ? = 0 and Ʃ𝐹 ? = 0 Ʃ ( 𝒓 × 𝑭 ) = 𝟎 Ʃ𝑀 ? = 0 Note that the axis (A), about which the moments of force are computed, may be any arbitrary point in the X-Y plane but either the center of gravity of the body or a joint centre of rotation is usually selected. Be aware that all the external forces must be included in the summations ( ) or the condition for static equilibrium will not be met. *** Frictional forces occur whenever two contacting surfaces attempt to move across one another. When at least one of the objects is moving, the situation is kinetic friction . When neither of the objects is moving, it is static friction . At the instant before movement takes place, maximum static friction is reached. The frictional force depends on two variables: 1) the normal force (F N ) measured in Newtons and 2) the nature of the surfaces involved known as the coefficient of friction (μ) which is unitless. Note: The frictional force is not dependent upon the surface (contact) area. The frictional force can be calculated using the following equation: 𝐹 𝑓?𝑖𝑐?𝑖?? = 𝜇 ??𝑎?𝑖𝑐 𝐹 ????𝑎? A second important equation in the study of friction is: 𝜇 ??𝑎?𝑖𝑐 = tan 𝜃 In some instances, friction is very desirable (e.g. rugby scrum). In others, we want to decrease friction as much as possible (e.g. luge). static kinetic time (s) starts to move

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 5 *** References: Knudson, D. V., & Morrison, C. M. (2002). Qualitative analysis of human movement (2 nd Ed.). Champaign, IL: Human Kinetics. Knudson, D. (2007). Fundamentals of Biomechanics (2 nd Ed.). Chico: Springer. Newton, I. (1947). Sir Isaac Newton’s Mathematical principles of natural philosophy and his system of the world (Andrew Motte’s translation revised by Florian Cajori). Berkeley: University of California Press. (Original work published 1687, Motte’s English translation 1729). Robertson, DGE. (2004). Introduction to Biomechanics for Human Motion Analysis (2 nd . Ed.). Waterloo, ON: Waterloo Biomechanics.

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 6 PART A – NEWTON’S LAWS OF MOTION (20 marks) Equipment: measuring tapes, 10-pound weight belt, artificial ice surface, a puck, a goniometer, masking tape, a penny, a bucket, a bean bag, blank paper Procedures: This portion of the lab will be carried out in a number of stations. Working in pairs, you will move through the various stations exploring Newton’s three laws of motion. As each station is completed, you will then fill out the questions for that station before moving on to the next activity. Station 1: Perform a standing long jump with and without a 10-pound weight belt around your waist and measure how far you jump. Try to jump with the same amount of force both times. Station 2: Slide a puck across different surfaces (artificial ice and plywood) and try to get it to stop the same distance on each surface. Pay attention to how hard you have to release the puck in each case. Station 3: Standing beside a wall, execute several vertical jumps using different degrees of knee flexion (30 , 45 , 60 , 75 and 90 ) and measure the height of each jump by sticking a piece of tape to the wall at the maximum height of each jump. Measure knee angles using a goniometer. Do not dip below the measured angle when jumping. Remove tape from wall when finished. Station 4: Do a standing long jump without swinging your arms and measure how far you jumped. Do another standing long jump but this time swing your arms and measure how far you jumped. Station 5: Hold your right hand next to your right ear, with your palm facing up. Place a coin on your elbow then quickly straighten your arm and try to catch the coin. Station 6: Place a bean bag in the bucket and, holding the handle of the bucket, spin the bucket around in a circle. Station 7: Stand with each of your feet on a separate sheet of paper. Carefully, start to run. Observe the paper. Questions for Part A: Station 1 Which law(s) of motion was (were) explored with this activity? First and third law Which technique allowed you to jump farther? Changing mass center height and increasing the vertical velocity by launching hands in the indented action and direction. Explain your findings using the appropriate law(s) of motion.

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APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 7 The body remains at rest unless a force acts on it , (1 st ) law. By applying force to the ground, GRF were able to oppose the movement to more forward. Station 2 Which law(s) of motion was (were) explored with this activity? All three laws Which surface required the most amount of force to reach desired distance and why? Ply wood, it has a fairly rugged surface meaning its coefficient of friction is higher. What type of external force do the different surfaces represent? Static friction as the puck was stationary, kinetic friction the puck begins its motion after limited by the friction of the wood, gravity, and normal force. Station 3 Which law(s) of motion was (were) explored with this activity? All three What is the relationship between the degree of knee flexion and the height of the jump? The depper the knee flexion the greater the height jumped. Explain your findings using the appropriate law(s) of motion. The body doesn’t move until the force of the legs act on the ground : 1 st law. As F= m*a, the amount of force produced to the gorund was proportionate to the jumpers mass and acceleration of legs: 2 nd law. Ground reaction forces resulting in the jump is the 3 rd law. Station 4 Which law(s) of motion was (were) explored with this activity? All three How far did you jump in each condition? 8 ft normal, 8.8ft with swing. Explain your findings using the appropriate law(s) of motion. 1 st law, Body doesn’t move until forces are acted upon. 2 nd law, adding more force from arm swing caused a farther jump. 3 rd law, GRF induced the action, by swinging the arms made this evident as the participant jumped farther. ______________________________________________________________________________________ Station 5 Which law(s) of motion was (were) explored with this activity? 1 st and 2 nd Did you catch the penny? Yes Explain your findings using the appropriate law(s) of motion.

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 8 1 st law, coin had inertia from gravity after the elbow was removed from below it 2 nd law, gravity (downward acceleration) as no normal force was active after the elbow is removed. ?? Station 6 Which law(s) of motion was (were) explored with this activity? 1 st and 3 rd Did the bean bag fall out? No Explain your findings using the appropriate law(s) of motion. 1 st law, net resultant force = 0 . 3 rd law, equal opposite reaction caused by the bucket and the circular motion all together help to keep the bean bag inside. Station 7 Which law(s) of motion was (were) explored with this activity? 1 st law, 3 rd law What happened to the pieces of paper when you started to run? Flew in the opposite direction. (backwards). Explain your findings using the appropriate law(s) of motion. 1 st law, the paper didn’t move until the force was acted on it. 3 rd , paper flew in the direction we applied force to (backwards) and ground reaction propelled us forward; Due to the coefficient friction of the shoe being higher than the smooth floor, the paper was moved by the shoe. ______________________________________________________________________________________ PART B – FORCE AND MOMENT OF FORCE OF THE BICEPS BRACHII (10 marks) Complete the following calculations. A moment of force is defined as the ability of a force to create rotation. In a static situation, a moment can also prevent rotation from occurring. For example, a moment of force at the elbow is required to prevent the forearm from extending. a. Given that the only muscle force acting on the forearm is the biceps brachii and that its angle of pull is 90˚ (forearm parallel to the ground), what moment of force is required to maintain static equilibrium ? Assume that the forearm and hand weigh 2.50 kilograms and their combined centre of gravity is 20.0 cm from the elbow. Also assume that the elbow is a frictionless joint (i.e. there is no moment of force caused by the elbow joint). Be sure to draw a free-body diagram and show your axes system. (2 marks)

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 9 M=fd M=(-9.81*2.5)(.2) = 4.905N/m b. Using the same information in part (a) c ompute the force in the biceps tendon assuming the insertion of the biceps brachii is 7.50 cm from the elbow. (2 marks) M=fd = 65.4 c. Using the same information in part (a) compute the moment of force caused by the biceps brachii if there was a 7.26 kilogram ball held in the hand and the hand is 38.5 cm from the elbow. (2 marks) M = 36.86 N/m 90 ° 7.50 cm 20. 0 cm

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APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 10 d. Using the same information in part (c) compute the force in the biceps tendon assuming the insertion of the biceps brachii is 7.50 cm from the elbow. (2 marks) F=491.467 90 ° 7.50 cm 20. 0 cm 38.5 cm

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 11 e. Finally, what is the tendon force of (c) if the angle of the elbow is increased so that the biceps angle of pull is 110˚, with the forearm still parallel to the ground? (2 marks) F = 461.853N 110 ° 20. 0 cm 38.5 cm 7.50 cm

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 12 PART C: DETERMINATION OF COEFFICIENT OF STATIC FRICTION VIA THE INCLINE PLANE METHOD (20 marks) Four conditions will be examined in this portion of the lab: 1) one puck + artificial ice surface; 2) one puck + plywood surface; 3) two pucks + artificial ice surface; 4) two pucks + plywood surface. In order to determine the coefficient of static friction for each of the conditions listed above, students will slide hockey pucks down an inclined plane. The formula to be used for this experiment is: 𝜇 ??𝑎?𝑖𝑐 = tan 𝜃 where μ static is the coefficient of static friction (unitless) and θ is the angle of friction in degrees. This formula indicates that the coefficient of static friction is equal to the tangent of the angle of friction. *Refer to Chapter 4 of the textbook Introduction to Biomechanics of Human Motion Analysis, 2 nd Edition by D. Gordon E. Robertson for the proof of this relationship. Equipment: 3 hockey pucks, artificial ice surface, plywood, and inclinometer Procedures: Each student should complete this part on their own and report their own data. Place a puck at one end of the incline plane and attach the inclinometer to the same end. Slowly incline the plane until the puck just starts to move. Refer to the video posted on Virtual Campus for proper technique. Record the angle at which the puck begins to slide down the inclined plane and repeat 9 more times. Calculate the mean (and standard deviation) of the 10 trials then use the mean to calculate the coefficient of static friction. Repeat this procedure for each puck-surface condition. Overall, 10 trials should be carried out for each of the 4 conditions, resulting in a total of 40 trials. Report your results in Table 1 below. Table 1. Results for Part B. (12 marks) Trial # Condition 1 1 puck + artificial ice surface Condition 2 1 puck + plywood surface Condition 3 2 pucks + artificial ice surface Condition 4 2 pucks + plywood surface Angle (°) μ static Angle (°) μ static Angle (°) μ static Angle (°) μ static 1 18 - 30 - 15 - 31 - 2 17 - 36 - 14 - 38 - 3 17 - 32 - 14 - 36 -

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APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 13 4 18 - 37 - 15 - 34 - 5 19 - 35 - 14 - 34 - 6 17 - 34 - 13 - 34 - 7 17 - 32 - 14 - 36 - 8 18 - 33 - 15 - 37 - 9 17 - 32 - 14 - 40 - 10 17 - 30 - 14 - 38 - Mean 17.5 0.315 32.9 0.647 14.2 0.253 35.8 Standard Deviation 0.671 - 2.256 - 0.6 - 2.482 - Questions for Part B: 1. Did the coefficient of static friction change when the weight was doubled? (1 mark) Yes - 0.315 to 0.253 - 0.647 to 0.721 2. Did the coefficient of static friction change when the surface changed? (1 mark) Yes the plywood had a higher coefficient compared to the artificial ice 3. What limitations are inherent with this method? (2 marks) Lack of precision created by human error from reading the measurement angle on the apparatus. In addition when tilting the board some force caused the bord to translate rather than rotate, causing the forces to transfer momentum to the puck.

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 14 4. Discuss and explain the relationship between μ static and weight. (2 marks) This relation ship is described through the equation F static =μ static ⋅ N Where: F static = is the force of static friction, μ static = is the coefficient of static friction, N is the normal force In this equation, the static friction force is directly proportional to the normal force and the coefficient of static friction. The normal force is essentially the weight of the object in most cases when it's on a horizontal surface. Therefore, the relati onship between μ static and weight (W) can be expressed as: F static =μ static ⋅ W This relationship indicates that the force of static friction depends on both the weight of the object and the coefficient of static friction between the object and the surface it's in contact with. If the weight increases, the force of static friction will also increase, assuming the coefficient of static friction remains constant. If the coefficient of static friction increases, the force of static friction will also increase for a given weight.

APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 15 5. Discuss and explain the relationship between μ static and surface. (2 marks) The coefficient of static friction (μ static) is a dimensionless quantity that describes the relationship between the force of static friction and the force pressing the surfaces together. This relationtion can be explan through material properties, surface roughness and surface treatment. Material Properties: Different materials have different coefficients of static friction. For example, rubber on dry pavement might have a different coefficient of static friction than metal on ice. Smoother surfaces often have lower coefficients of static friction than rougher surfaces. Surface Roughness: The roughness of the surfaces in contact affects the coefficient of static friction. Rough surfaces tend to have higher coefficients of static friction compared to smooth surfaces. Surface Treatment: Surface treatments or coatings can alter the coefficient of static friction. For instance, adding a lubricant can reduce friction, resulting in a lower μ static. PART D: USING SIMULATION SOFTWARE TO EVALUATE FRICTIONAL SITUATIONS Working individually or in pairs, spend at least 10 minutes using the Ramp: Forces and motion simulation applet to examine the relationships between force vectors for the friction (wood) and nofriction (ice) situations on the level surface and the inclined plane (ramp). This applet is available here: https://phet.colorado.edu/sims/cheerpj/motion-series/latest/motion- series.html?simulation=rampforces-and-motion . The following forces should be examined: 1) applied force 2) frictional force Note: When using the program, you should select the “Force Graphs” tab at the top because this will allow you to see a graph of the relationship between the frictional and applied forces. (The normal force and weight vectors may be cut off. You can examine them under the “Friction” tab later if you’d like). Then, you can play around with the following options: • Whether or not to include a free body diagram. • Which frictional situation you would like to evaluate (Ice vs. Wood). • Which vectors to include (It is recommended that you only include the “force vectors”). • Whether the walls are brick or bouncy (Not important either way for this lab). • The object’s starting position (For the level surface, you may want to start as far to the right as possible and then apply your force negatively. That way, your frictional force will be positive, and when the Force vs. Time graph appears at the bottom of the screen, the frictional force curve will match the relationship in the “standard model of friction” seen above. For the ramp, you may

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APA 2315 – Introduction to the Biomechanics of Human Movement University of Ottawa 16 want to start with the box part way up the ramp, and apply the force in the positive direction, up the ramp.) • The ramp angle (For a level surface, set it to zero degrees; for the inclined plane, select any angle greater than 25 degrees so that you can really see the relationships between the forces) • Which object you would like to use (Use the crate for all situations, then, if you have time, you can use the other objects) Once you have selected your conditions, press the play button, but make sure you are in “record” mode. Then, slowly increase your applied force by dragging the arrow beside the graph (if you set your object up as described above, this will be in the negative direction on the level surface and in the positive direction on the ramp). Examine the relationships between the various forces. There is nothing to submit for this portion of the lab. It is designed to help you better visualize the concepts associated with friction. On the next page, you will find sample screenshots of the wood and ice situations on the level surface. Wooden surface Icy surface

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Lab 7 - kinetics

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