Biomechanics Exam 3

A quarterback is chased from the pocket on a crucial 4th down play. He has a mass of 85kg and is running toward the first down marker at 9m/s. The opposing linebacker (mass=100kg) meets him head-on with a velocity of -8m/s. The linebacker wraps up the quarterback during their collision. What is their resulting velocity after the collision?

-0.19 m/s

A jumping person (m = 57 kg; vi = 0) has an average GRFy of 750 N for 0.52 seconds. How high do they jump?

0.15 m

What is the moment of inertia of an object about an axis if there are three point masses (m1 = 1.20 kg, m2 = 1.75 kg, m3 = 1.95 kg) located at r1 = 0.10 m, r2 = 0.15 m, and r3 = 0.31 m distance from the axis of rotation (in kgm2)?

0.239

Which axis of rotation has the lowest moment of inertia?

D - Longitudinal

A 0.3 kg basketball is dropped from a height of 2.2 m. Video analysis is used to determine that the ball bounced to a height of 0.91 m. What is the coefficient of restitution between the floor and the ball?

0.58

During walking, the order of magnitude of GRF from highest to lowest is

1) vertical 2) anteroposterior 3) mediolateral

What is the average impact force exerted by the glove on the baseball?

1,898.4

What is the net moment (torque) at the ankle joint during the swing phase of walking? Given the following information: Foot mass =1.16 kg ax=-1.35 m/s2 ay=7.65 m/s2 ICM=0.0096 kg-m2 αz= -14.66 rad/s2

1.17

If an object achieved an angular acceleration of 37 rad/s2 due to a torque of 46 Nm, what was the object's moment of inertia (in kg.m2?

1.24

A jumping person (m = 57 kg; vi = 0) has an average GRFy of 750 N for 0.52 seconds. What's their vertical takeoff velocity?

1.74 m/s

Compute I in the figure. ICM is the moment of inertia about an axis passing through the center of mass of the object.

12.1

As an expert biomechanist, you've just been hired by Schuttto supervise a team designing a safer helmet to reduce concussions in NFL football players. The team presents you with two models which simulate a player's head hitting the inside of the helmet. During both simulations, the helmet is hit with the same external force and the model of the head is assumed to have a mass of 3.6 kg. The first simulation shows that the exterior of Helmet 1 buffers some of the force so that the player's head is moving at 5 m/s immediately after application of the external force. The inside of Helmet 1 is cushioned so that the cushion gives for .15 seconds before the head comes to rest. What is the force transferred to the player's head in the first simulation?

120 N

How much work does the catcher do on the baseball during the catch (J)?

151.9 J

The displacement of the baseball due to the deformation of the catcher's glove and the movement of the catcher's hand is 8 cm in a horizontal direction from the instant it first makes contact with the glove until it stop. How much kinetic energy does the baseball possess just before it strikes the glove (J)?

151.9 J

What would be the force (in N) exerted by a spring with a stiffness of 100 N/m that was compressed 0.02 m? What would be the strain energy stored in this compression?

2 N strain energy = 0.02

Kate is taking part in jumping drills at the start of the University of Georgia basketball season to measure her maximum vertical jump height. She is performing non-counter movement jumps from a force platform which enables her vertical ground reaction forces to be recorded. She has a mass of 73 kg. For a particular jump, the trainer recorded an average vertical ground reaction force (FG,y) of 2130 N applied over a duration of 185ms. What is the average power produced by the legs to increase the body's kinetic energy (in W)? What is the height Kate jumped for this trial?

2,533 W 0.55 m

If the mass of the foot is 1.16kg and the horizontal and vertical acceleration of the foot are -1.35 m/s2 and 7.65 m/s2, respectively, what is the foot's vertial joint-reaction force (in N)?

20.3 N

A football fan is trying to find her seat. Her seat is in the 90th row. The difference in height between the seats is 35cm. The fan weighs 800N. How much work does she do by climbing to the 90th row (in J)?

25,200 J

How much power is generated if she climbs to her seat in 90 seconds (in W)?

280 W

What would be the centripetal force of an object (m = 7 kg) rotating about a radius of 1.5 m at 1.8 rad/s?

34.02

An ultimate Frisbee player (body mass of 54 kg) sprints at 7.1 m/s and makes a quick turn to her right. In the stance phase during this turn, her vertical acceleration is 5.0 m/s2 and her horizontal deceleration is -2.0 m/s2. If the static coefficient of friction between her foot and the turf is 0.8, how small of a radius (m) can she have on her turn not to slip? Assume that air resistance is negligible.

4.3 m

A person (mg = 800 N) walks 1000 m on a 45° uphill slope. How much mechanical work (in J) is required to lift the object up the hill?

565,680 J

The second simulation shows that the exterior of Helmet 2 buffers some of the force so that the player's head is moving at 5.3 m/s immediately after application of the external force. After the force reaches the head, the inside of Helmet 2 is cushioned so that the cushion gives for .22 seconds before the head comes to rest. What is the force transferred to the player's head in the second simulation?

86.7

For any set amount of applied elbow flexor muscle force, the largest torque is produced when the muscular line of pull is at an angle of _____ from the ulna.

90 degrees

Eddie imparts side spin on the ball to try and fool the goal keeper by striking it with the inside of his kicking (right) foot (see the figure below). Which direction the ball will move to eventually?

Left

A 3kg mass is accelerating at 2m/s2 in a straight line. How much force is pushing the mass?

6

If all of the following objects are at rest, which will exhibit the highest potential energy A .15 kg baseball stuck above a speaker 50 meters above the ground A 6 kg bowling ball being held 1 meter above the ground A .4 kg basketball held above the head of a 2.1-meter-tall player A .05 kg wiffle ball set atop a .75-meter-tall tee

A .15 kg baseball stuck above a speaker 50 meters above the ground

If the mass of the foot is 1.16kg and the horizontal and vertical acceleration of the foot are -1.35 m/s2 and 7.65 m/s2, respectively, what is the foot's horizontal joint-reaction force (in N)?

-1.57 N

An ice-skater is spinning counter-clockwise and changes her arm configuration during the routine. At a given instant her angular acceleration is 1.4 rad/s2 and her angular velocity is 2.8 rad/s. If her current moment of inertia is 5.6 kg.m2, what is the rate (kg.m2/s) at which her moment of inertia is changing? Assume ice is almost frictionless and applies no torque on the skater.

-2.8

During a Bulldogs baseball game, the catcher (mass = 90kg) was analyzed to determine the effects of catching fast balls. He caught a 45m/s pitch over a 0.3 second time period. The mass of the ball is 0.15kg. How much force was created by the impact of the ball against the glove?

-22.5 N

A 115 kg football player is running toward another player at 14 m/s. How much average force (in N) needs to be applied over 2.0 seconds to bring him to a stop?

-805 N

Which of the following best describes inertia?

A measure of an objects resistance to a change in motion

During the stance phase of human walking, which lower limb joint usually has the greatest muscle power?

Ankle

During diving, when the diver has left the board (vertical line hash mark in the figure), what could happen to the local and remote angular momenta for different body segments?

Both local and remote angular momenta can change for all segments

During figure skating, a skater can manipulate angular velocity despite no external torques being applied to her. Which mechanical principle can explain this phenomenon?

Conservation of angular momentum

Describe key factors affecting stability.

Factors that affect stability are wide base support, low center of mass, and increasing the amount of contact points with the ground. Friction is also a factor that increases stability. The greater the coefficient of friction, the more stable a body is. High levels of inertia also increase stability. Increasing stability is important for future bone and joint growth/health. Balance is important,

The mechanical advantage of a third-class lever is always greater than the mechanical advantage of a second-class lever.

False

Your team recorded the lower extremity motion and force in a walking study. Given the foot acceleration and force information shown in the diagram, find the horizontal joint-reaction force at the ankle: Fax Find the vertical joint-reaction force at the ankle: Fay Find the net moment (torque) around the ankle.

Fax = -106.9 Fay = -517.5 net moment torque = -80.0

Which of the following statements best describes pressure force?

Force per unit area

Which helmet design would you suggest is safer/more effective in reducing concussions if concussions are caused primarily by force application to the head?

Helmet 2

Try pushing a heavy book across a table. Is it easier to get it started moving or keep it moving?

It's easier to keep it moving

Which term best represents energy resulting from motion?

Kinetic energy

If a collision between two bodies results in a coefficient of restitution of 1.0, this collision can be described as:

Perfectly elastic

Describe magnus effect and give an example in sport.

The magnus force is a generation of a sidewise force on a spinning cylindrical or spherical solid immersed in a fluid when there is relative motion between the spinning body and the fluid. The magnus effect is when a ball is flying through the air and it is spinning with air moving around it, creating a curve in the trajectory of the ball. In this example, the object is the ball and the fluid is the air. Another example is kicking a soccer ball with some spin. This effect can only occur if the object is spinning.

In an experiment on patients with Parkinson's disease, patients' gait data were collected, and joint angles over gait cycle were plotted below. a. Use the kinematics and kinetics knowledge you learned from this class, explain what are the major abnormalities in PD patients walking pattern. b. Relating to the concept of vigor and neural mechanism discussed in this course, what are the possible reasons that cause these deficits?

The major abnormalities in PD patients walking pattern are extended stance phases, slower velocity with shorter strides, and taking more steps per minute. In relation to kinetics, the PD patients are producing less force which accounts for the abnormalities in their joint movements. The lack of force here is primarily caused by lack of communication between the neural signals that are prompting muscle contraction and the neuromuscular junctions that cannot process these signals. In relation to kinematics, there is a shuffling motion that is created through the gait cycle, which turns out to be much safer for PD patients. This shuffle is safer, because it keeps the patient in the non-supportive phase for as little time as possible. With this shuffle however, turning around and walking long distances is very difficult on these patients. Along with this shuffle, PD patients also experience decrease ankle plantarflexion, decreased knee extension, as well as decreased hip extension during shuffle motion. There are many different joint torques that can be looked at during the gait to further observe PD patients' joint function. The ankle torque in patients with PD is lower than the control group for 60% of the gait cycle. The hip torque in PD patients was actually higher throughout the cycle. The knee torque was lower in PD patients for the first quarter of the gait cycle, but then it was higher in the middle 35% and lower in the final 40%. The different amounts of power exerted from these joints can also help us to further observe these patients. The ankle power in PD patients is significantly lower than the control group. The knee power is higher at 60% of the gait cycle. The hip power is higher than control group for first 40%, then significantly lower than the control group at 60%. There are many deficits in patients with PD, and a lot of these can be explained by the deterioration of the basal ganglia.

Use the kinetics knowledge you learned from this class, analyze the following free-body diagram of a person lifting an object, and explain what are the factors for a good lifting strategy to avoid back injury

The required torque to lift this box at a distance of 40 cm from the axis of rotation can be found using 111 N x 40 cm. This gives us a torque of 4.44 Nm. In order to minimize back strain, the proper way to lift this box would be to decrease the distance of the box from the body along with decreasing the amount of required torque. This will help to lift the box more efficiently, and to minimize back strain, especially on the lower spine. Overall good strategies for lifting consist of maintaining a neutral spine, lift from the leg muscles, and to keep the weight close to the body. Maintaining a neutral spine will help us to avoid rounding our backs. Lifting from the leg muscles will help us to avoid lifting from the back. Keeping the weight close to the body will help avoid additional strains from lack of stability.

During a countermovement jump, there is a period of time where forces acting on the person from the ground are less than body weight (see figure below). Which of the following statements best explains this observation?

Velocity is increasing in the negative direction.

Consider a situation when only two torques are acting about the elbow: torque due to the biceps brachii and torque due to resistance (i.e., weight). During an elbow flexion exercise, if the biceps brachii generate 250 N of force with a moment arm of 0.05 m, what type of contraction would occur if the resistance force was 62 N (moment arm = 0.2 m)?

concentrtic

During running along a straight line at a steady velocity (acceleration = 0), the average braking and propelling impulses are equal (see Figure A below). In Figure B, the person showed

decreased acceleration and increased negative impulse in the breaking phase.

Where to place COG to get a quick start in walking/running?

front edge of BoS

Backspin in a golf ball

helps to keep the ball in the air longer

A non-Biomechanics student is trying to move a desk. He pushes on the desk with a force of 100N at an angle of 330°. The desk weighs 75N and the coefficient of static friction is 0.70. What is his force applied horizontally (in N)? What is the static friction of the desk (in N)? Did he move the desk?

horizontal applied force = 86.6 N static friction = -87.5 N Move the desk? = No

Harry (80 kg) is riding a bike (8.5 kg) on wet concrete. He wants to go around a circular path with a radius of 10.5 m but does not want to fall. The coefficient of static friction between the bicycle tire and the wet concrete is 0.5. Assume that the both tires provides the propulsive force to overcome air resistance and that the vertical and lateral ground reaction forces are both equally distributed between the two tires. The frontal surface area of the rider and bike is 0.54 m2, the drag coefficient of the rider and bike is 0.82, and the density of air is 1.2 kg.m3. How fast can he go around the curve without slipping if his linear speed remains constant (in m/s)? What is the centripetal force (in N) Harry experiences at this speed? What is the drag force (in N) Harry experiences at this speed?

how fast? = 7.17 m/s centripetal force = 433.3 N drag force = 27.2 N

The drag force is a component of fluid resistance that always acts opposite to the motion of the person. This force is not proportional to which of the following:

mass of the person

Consider the free body diagram for the elbow joint for a biceps curl exercise. Up is positive. If d1 = 0.045 m, d2 = 0.16 m; d3 = 0.5 m, using static analysis solve for the moment at the elbow (in Nm). Using static analysis solve for the torque of the ball (in Nm). Using static analysis solve for the net muscle force, Fm (in N).

moment at elbow = -2.59 Nm torque = -101.3 net muscle force = 2,305 N

In the middle of the swing phase of a gait cycle in brisk walking, a walker had the horizontal acceleration ax= 1.7 m/s2, the vertical acceleration ay= 8.2 m/s2, the moment of inertia of the foot about its center of mass is ICM=0.001 kg-m2 and the angular acceleration of the foot is 𝛼𝑧= -25 rad/s2. The mass of the foot is 1.3 kg The moment from horizontal joint reaction force is _______ N.m. The moment from vertical joint reaction force is _______ N.m. Given the acceleration about the center-of-mass and other computed forces, the muscle torque acts on the ankle joint is _______ N.m.

moment from horizontal = 0.15 moment from vertical = 1.64 muscle torque = 1.77

During a basketball throw-in, the player's triceps contract to propel her forearm into launching the ball (mball= 0.45 kg). The player's forearm has a mass of approximately 4.5 kg, the center of mass of the forearm is located 0.17m from the elbow joint center, and the distance along the forearm from the elbow joint center to the ball is approximately 0.35m (shown in diagram). As the forearm begins to rotate, the radius of gyration is .20m. Previous muscle studies in basketball shooting have indicated that, on average, the triceps act a point 0.013 m behind the elbow joint center and produce a force of 750 N. The moment of inertia ICM of the forearm is _______ kg.m2 The torque of the ball is __________ N.m. The torque of the forearm is __________ N.m. The torque of the triceps is __________ N.m. What will be the angular acceleration of the player's forearm as she performs the throw (in rad/s2)?

moment of inertia = 0.18 torque of ball = 1.54 torque of forearm = 7.48 torque of triceps = -9.75 angular acceleration = -3.89

During the second half of elbow flexion, the net muscle torque will be ______, and the power will be _____.

negative, negative

During the first half of elbow extension, the net muscle torque will be ______, and the power will be _____.

negative, positive

Which of the following makes the statement FALSE? Increasing the amount of knee flexion that occurs during landing from a jump ________

requires less quadriceps muscle fiber lengthening

When walking/riding uphill, do we experience larger or smaller friction compared to that on a flat surface?

smaller

Which of the following does not affect the magnitude of static friction force before it reaches to the maximum value?

the mass of the object

During running, the dynamic coefficient of friction can be calculated using which formula (Fy= anterior/posterior; Fx = medial/lateral; Fz = vertical force components)?

u = Fy/Fz

What is the COM of the arm in this diagram (x value)? y value?

x = 4.34 y = 5.47

Explain the difference between elastic and inelastic collision using the concept of momentum. Use equations and examples if needed.

· A collision is when momentum or kinetic energy is transferred from one object to another. An inelastic collision occurs when two objects collide and do not bounce away from each other. The momentum in this inelastic collision is conserved, because the momentum of both objects before and after the collision stays the same. However, the kinetic energy is not conserved due to some of it being converted into sound, heat, and deformation of the objects. Thus, in an inelastic collision momentum is conserved but kinetic energy is not. An elastic collision is when two objects collide and then "bounce" apart. In an elastic collision, both momentum AND kinetic energy are conserved. Almost no energy is lost to sound, heat or deformation. An example of this would be your car bumper. The car's bumper can deform and bounce back with a small enough kinetic energy caused by a slow collision, transferring all the energy directly back into motion. Now, with all this information at hand, we use equations with conservation of momentum to solve these collision problems. In a perfectly elastic system, we use m1u + m2u = m1v1 + m2v2. We use this because all of the momentum is conserved in elastic collisions. In an inelastic system, we use m1v1 + m2v2 = (m1 + m2)v3. We use this equation because not everything is conserved in an inelastic collision. The coefficient of restitution is used to calculate the relative speeds before or after collision. It is represented by E= V1f-V2f/ V1i- V2i.

Explain the law of conservation of angular momentum. Use an example in sport.

· Conservation of angular momentum occurs when gravity is the only external force acting on an object. When gravity is the only external force, the angular momentum stays constant. This is due to the gravitational force acting through the center of mass of an object, or point of rotation, thus not producing a torque. An example of conservation of angular momentum is seen in ice skating. When an ice skater tries to execute a spin, the net torque is 0. This is because there is little friction between her skates and the ice, and the friction is exerted very close to the pivot point. The skater also spins faster when her arms are pulled closer to her body. If we consider the skater an isolated system, then when the moment of inertia of the skater decreases, the angular velocity increases.

Explain succinctly the differences between: moment (torque) and moment of inertia. Use equations, examples and specify units if needed

· Moment of inertia is an objects resistance to rotation or angular motion and is found by the mass x the radius of gyration squared (k^2). Each axis has its own moment of inertia associated with it, because rotation can occur about multiple axes. Moment of inertia is measured in kgm^2. Torque is dependent upon the amount of force and the length of the moment arm. Torque is found by the force x the distance of the moment arm (r ). Torque is measured in Nm.

Explain the difference between momentum and impulse and their relationship. Use equations, examples, and specify units if needed.

· Momentum is mass x velocity or P=mv. Momentum is the measure of force and time and it is measured in kgm/s. On the other hand, impulse is force x time interval or Delta p = F (delta t). Impulse is the change in momentum and is measured in Ns. Impulse has an inverse relationship with force applied; so that when impulse increases, force applied decreases. An example of this would be with the use of an air bag in a vehicle. When the driver gets into an accident, their momentum carries them forward into the steering wheel. By putting the airbag on, a smaller force is exerted over a longer period of time to change the momentum to stop. Without the airbag, a large force is exerted over a short time which will cause more damage to the driver.

Explain the difference between kinetic energy, potential energy, and elastic energy, and how they convert from one to another. Use equations and examples if needed

· Potential energy is energy that is capable of doing work given a body's position. It is equal to (mgh). Kinetic energy is energy in motion. It is equal to ½(mv^2). Elastic energy is the energy stored due to the deformation of a material. It's equal to ½ *k x delta x^2). All of these energies are converted from one to another in order to keep the total energy of the closed system constant. The total energy of the system can be represented by TE = PE + KE = mgh + ½(mv^2). Potential energy and kinetic energy are inversely related; thus, if potential energy increases, kinetic energy will decrease.

Describe the difference among major classes of levers and give an example in the human body for each class.

· There are three classes of levers; 1st, 2nd, and 3rd. The first class levers have effort force and resistance force ono opposite sides of the fulcrum. An example of this is the skull balancing on the spine. The second class levers have the effort and resistance force on the same side of the fulcrum, and the resistance arm is less than the effort arm. An example of this would be the lower leg, ankle and foot complex. The third class levers have the effort and resistance forces on the same side of the fulcrum, and the resistance arm is greater than the effort arm. An example of this is the upper arm and forearm (Along with the majority of the muscolosketal system). 2nd class levers provide strength and stability and are slow to move. 3rd class levers favor speed and range of movement.