Biomechanics 2

A basketball is released with an initial velocity of 8 m/s at an angle of 60° from a play's hand holding it 2.2m above the ground. Determine the following quantities, assuming air resistance is negligible. Find the ball's horizontal distance from the player at 0.5 second after it is released (in m).

2 4 x 0.5 = 2.0 m

Mark McGwire's last home run left the bat with a speed of 50m/s at an angle of 35°. What is the vertical component of the initial velocity? I think she meant 30 degrees

25 m/s Sin(Theta) = (opposite / 50 m/s) Sine(30) x 50 m/s = opposite = 25m/s

The horizontal velocity of a shot put is slowed down by gravity 9.81 m/s every second it is in the air.

False

Holding the hand in a fixed position and drawing an imaginary O in the air with the thumb is best described as

circumduction

When the body is in anatomical position, the thumb is on the ________ side of the hand.

lateral

You collect the following data from a person walking using a motion capture system. Using the table, calculate the angle of the leg at frame 4 (in degrees).

leg =tc and lm, thigh = gt and fc Delta Y= 50 - 19.7 delta X= 121-95.6 Tan-1(50-19.7 / 121- 95.6) = 50.0

During running 100 m, a runner runs from the 40- to 80-m mark in 330 frames of a video record. If the video camera recorded data at 60 fps, how fast was she running during this interval?

7.27 m/s time elapsed = 330/60 = 5.5 sec distance covered = 80-40 = 40 m time it took = 40/5.5 = 7.27m/s

Neglect air resistance, find how far does his center of mass displace horizontally between take-off and landing (in m).

8.29 Range = (Vo2 x sin(2theta)) /2g + (Vcos(theta) x (sqrt (Vo x sin(theta))^2 + 2gh)/g

When one returns to the fundamental position from the anatomical position, the proximal radioulnar joint in the elbow makes.

pronation

During the support phase of walking, the absolute angle of the thigh has the following angular velocities:

(29.4 - 32.1) / (.65 - .6167) = -81.1

A baseball runner slides to a stop over home plate. Her running velocity is 4 m/s, and then goes into a 0.5 second slide to stop. What is her acceleration during the sliding motion (in m/s2)?

-8 m/s2 Vf = Vi + at 0 = 4+ a(0.5)

During an activity, if the initial angle (qi) of a segment was 180°, and the final angle (qf) was 100°, what was the angular displacement?

-80 angular Final - angular initial = angular discplacement

A 7.26-kg ball is thrown with a velocity of 14 m/s at an angle of 35° from a height of 2.2 m. Neglect air resistance, determine the time to apex (in s).

.82 14sin(35) = 8.03 (find vertical velocity) Apex = (8.03 / 9.8) = 0.82sec

A 7.26-kg ball is thrown with a velocity of 14 m/s at an angle of 35° from a height of 2.2 m. Neglect air resistance, determine the time from the apex to the ground (in s).

1.06 H = 1/2 gt^2 T = (sq root) 2H / g = 2(5.49) / 9.8 = 1.05sec

A golfer increases the angular velocity of the head of his club over 0.25 sec from 450°/sec to 625°/sec at contact with the ball (club length is 1.2 m; club loft 38 degrees). Determine the following quantities:c. the linear (tangential) velocity at ball contact ________m/s

1.2 x 625(pi/180) = 13.09

A golfer increases the angular velocity of the head of his club over 0.25 sec from 450°/sec to 625°/sec at contact with the ball (club length is 1.2 m; club loft 38 degrees). Determine the following quantities:b. the tangential acceleration during this time ________ rad/ s2

1.2 x 700(pi/180) = 14.66

A child's vertical takeoff velocity when jumping on a trampoline is 6.5 m/s. Assuming takeoff and landing heights are the same, how long is the child airborne (in seconds)?

1.33 2(Vyi) / g = answer (changes velocity)

You collect the following data from a person walking using a motion capture system. Using the table, calculate the angle of the thigh at frame 4 (in rad).

1.35

Your group project team members collected the following data by recording an athlete running. Now try to derive the velocity (m/s) for frame 2 using the finite central difference method.

10.91 Vyi = (Yi +1 - Yi -1 ) / 2 x (change in time) 0.36 - 0.00) / ( 0.033 - 0.000) = 10.91

Calculated the absolute angle of θthigh.

108.44

The figure below shows a discus throw in which an athlete rotates at high angular velocities before releasing the discus. The angular velocity of the athlete's arm at the point of release is 25 rad/sec and the athlete's arm length is 1.4 m (see figure). The release angle is θ=60° and height of release is h = 2.2 m (see figure) Find the horizontal displacement (R) of the discus put when it lands (in m/s).

109.51 R = (1060.88 / 19.6) + ((17.5 x sq rt (918.75 + 43.12)) / 9.8 = (54.13) + 55.38 = 109.51

Calculated the knee flexion angle

137.6

A golfer standing in a tee box that is 4m above the fairway increases the angular velocity of the head of his club over 0.5 sec from 400°/sec to 600°/sec at contact with the ball (club length is 1.4 m; club loft 35 degrees). Determine the linear (tangential) velocity at ball contact ________m/s

14.7

Your group project team members collected the following data by recording an athlete running. Now try to derive the velocity (m/s) for frame 3 using the finite central difference method.

16.06 Vyi = (Yi +1 - Yi -1 ) / 2 x (change in time) (0.68 - 0.15) / (0.050 - 0.017)

You collect the following data from a person walking using a motion capture system. Using the table, calculate the linear (tangential) velocity of the greater trochanter at frame 2 using the central difference formula.

166.4

Your group project team members collected the following data by recording an athlete running. Now try to derive the velocity (m/s) for frame 4 using the finite central difference method.

17.94 Vyi = (Yi +1 - Yi -1 ) / 2 x (change in time) (0.97 - 0.36)/ (0.067 - 0.033)

A basketball is released with an initial velocity of 8 m/s at an angle of 60° from a play's hand holding it 2.2m above the ground. Determine the following quantities, assuming air resistance is negligible. Find the ball's vertical velocity 0.5 second after it is released (in m/s).

2.03 6.93 - (9.8 x 0.5) = 2.03 m/s

A 7.26-kg ball is thrown with a velocity of 14 m/s at an angle of 35° from a height of 2.2 m. Neglect air resistance, determine the range of the throw (in m).

21.56 Range = (𝑣0^2 𝑠𝑖𝑛(2𝜃)) / 2𝑔. +. (𝑣0 cos⁡(𝜃)×√((𝑣_0 sin⁡(𝜃))^2+2𝑔ℎ))/𝑔 9.40 + (11.47 x (64.48 + 43.12) / g ) 9.40 + (11.47 x 10.37) / g 9.40 + (12.14) = 21.54

Your group project team members collected the following data by recording an athlete running. Now try to derive the acceleration (m/s2) for frame 3 using the finite central difference method.

213.09 a_yi=(Vyi+1 - Vyi-1 )/2∆t

A golfer standing in a tee box that is 4m above the fairway increases the angular velocity of the head of his club over 0.5 sec from 400°/sec to 600°/sec at contact with the ball (club length is 1.4 m; club loft 35 degrees). How far did his drive go (in m)?

25.4

The figure below shows a discus throw in which an athlete rotates at high angular velocities before releasing the discus. The angular velocity of the athlete's arm at the point of release is 25 rad/sec and the athlete's arm length is 1.4 m (see figure). The release angle is θ=60° and height of release is h = 2.2 m (see figure). What is the tangential velocity of the disc at the point of release (in m/s)?

35 Angular velocity = w x r = 25 x 1.4 = 35

A basketball is released with an initial velocity of 8 m/s at an angle of 60° from a play's hand holding it 2.2m above the ground. Determine the following quantities, assuming air resistance is negligible. Find the horizontal component of the ball's initial velocity (in m/s).

4 Cos(60deg) x 8 m/s =

A basketball is released with an initial velocity of 8 m/s at an angle of 60° from a play's hand holding it 2.2m above the ground. Determine the following quantities, assuming air resistance is negligible. Find the ball's horizontal velocity 0.5 second after it is released (in m/s).

4 m/s stays constant

A basketball is released with an initial velocity of 8 m/s at an angle of 60° from a play's hand holding it 2.2m above the ground. Determine the following quantities, assuming air resistance is negligible. Find the ball's height above ground 0.5 second after it is released (in m).

4.44 2.2 + [ 6.93 x 0.5 - 1/2 (9.8 x (0.5)2)] = 2.2 + (3.465 - 1/2( 2.45) ) 2.2 + (2.24) = 4.44m

A golfer standing in a tee box that is 4m above the fairway increases the angular velocity of the head of his club over 0.5 sec from 400°/sec to 600°/sec at contact with the ball (club length is 1.4 m; club loft 35 degrees). Determine the angular acceleration during this time _______ °/s2

400

Mark McGwire's last homerun left the bat with a speed of 50m/s at an angle of 35°. What is the horizontal component of the initial velocity? meant 30 degrees

43.3 m/s Cos(theta) = (adjacent / 50 m/s) Cos(30) x 50m/s = adjacent = 43.3 m.s

During the latter portion of the swing phase of a walking stride, the knee is extended from 65° to 5° over a time period of 0.12 s. What is the angular velocity in °/s?

5-65 / .12 = -500 Change in angular position / change in time = (5 - 65) / ( 0.12-0) = - 500 deg/s

A 7.26-kg ball is thrown with a velocity of 14 m/s at an angle of 35° from a height of 2.2 m. Neglect air resistance, determine themaximum height of the ball (in m).

5.49 S(up) = Vy / 2g (8.03)^2 / (2x9.8) = 3.29 m H (maximum height) = h + S(up) = 2.2 + 3.29m = 5.49

A kicked football left the foot of a punter with a vertical velocity of 24.0 m/s and a horizontal velocity of 20.0 m/s. What was the direction (angle relative to the horizontal) of the initial linear velocity?

50.2° Tan(theta) = 24/20

If the initial velocity of an object is vi=10 m/s and it undergoes acceleration as shown in the figure below, what is its final velocity, vf ?

52

A basketball is released with an initial velocity of 8 m/s at an angle of 60° from a play's hand holding it 2.2m above the ground. Determine the following quantities, assuming air resistance is negligible. Find the vertical component of the ball's initial velocity (in m/s).

6.93 sin(60 deg) x 8 =

A golfer increases the angular velocity of the head of his club over 0.25 sec from 450°/sec to 625°/sec at contact with the ball (club length is 1.2 m; club loft 38 degrees). Determine the following quantities:a. the angular acceleration during this time _______ °/s2

625 - 450 / .25 = 700

A runner completes 2 laps around the Spec Towns Track (400m/lap). What is the distance traveled (in m)? What is the runner's displacement (in m)?

800m, 0m

A long jumper's take-off velocity is 10 m/s at an angle of 20o from the horizontal. Her center of mass is 1 m above the ground at take-off and is 0.2 m above the ground at landing. Neglect air resistance, find what is her take-off horizontal velocity (in m/s).

9.40 Cos(20) = (Vy / 10)

A golfer standing in a tee box that is 4m above the fairway increases the angular velocity of the head of his club over 0.5 sec from 400°/sec to 600°/sec at contact with the ball (club length is 1.4 m; club loft 35 degrees). Determine the tangential acceleration during this time ________ rad/ s2

9.79

A golfer increases the angular velocity of the head of his club over 0.25 sec from 450°/sec to 625°/sec at contact with the ball (club length is 1.2 m; club loft 38 degrees). Determine the following quantities:d. If he is standing in a tee box that is 5m above the fairway how far did his drive go?

??? 13.08^2 sin(2x38) / 2 (9.81) + 13.08cos(38)x = 20.68

Describe basic linear kinematic variables in gait analysis.

A stride is the distance person travels between the same heel. A step is he distance between he two feet 1 stride = 2 steps. The Toe-out angle -angle of the foot relative to the line of progress and gives information about the internal / external rotation. The cadence is the number of steps at a given time normal range ~100-115 steps/min. The speed is the momentary speed during walking. Last is the step.

In a study on stroke patients' walking pattern, patients were asked to walk on a treadmill and their kinematic and EMG data were collected and the results were presented in the following graphs. Explain a. What are the major kinematic and EMG features in stroke patients' gait? b. What would be your recommendations for them to correct these deficits?

A) Reduced plantar and knee flexion on the side of the stroke affect , and less EMG .activity , less muscle activity on the hamstring. One side is weaker forward proportion and weaker stance support than the other. asymmetric gate patterns, because stroke affects one side B) Increase bas fitness level overall. Estimate the benefits of muscles and leg, and to increase the daily walking activity. rehab and PT inc. dorsiflexion

In the figure below, θ_trunk is a ____ angle

Absolute

If angular acceleration is negative, which of the following statements could be true?

Angular velocity is positive and decreasing.

Describe what is a projectile motion.

Any object that has a period of no support, phase of non- support, and gravity and air resistance are the only forces.

If a gymnast leaves the ground with a vertical velocity of 9.81 m/s when doing a back flip, where in her trajectory will her center of mass be 1.0 seconds later?

At the apex

Describe centripetal acceleration and factors influencing centripetal acceleration.

Centripetal (radial) acceleration is a component of angular acceleration directed toward the center of curvature, given a fixed radius of rotation, that indicates change in direction. It is a linear quantity and always directed inward, toward the center of a curved path. mass and speed of the object along with the radius it is moving aorund. Increase in tangential velocity .... velocity will increase centripetal acceleration.

If a stroke occurs in the left side of the brain, the right side of the body will be affected, producing hemiparesis/hemiplegia on the right side of the body. The affected side of the body is the ______ side.

Contralesional

When the shoulders return to a neutral position from being shrugged, the scapulae undergo

Depression

A runner moves along the path followed by the dotted line. The dotted line is _____, and the solid line is _____. (picture)

Distance, displacement

Flexion is more difficult in supinated posture of the forearm.

False

Describe key factors that influence the movement of a projectile.

Gravity and air resistance (air-drag) affect the movement of a projectile.

Which of the following statements is TRUE?

If two projectiles are released with the same horizontal velocity, the one with the largest vertical velocity at release will land further away.

During walking, children with cerebral palsy typically exhibit higher amount of ___________ at the hip.

Internal rotation

Describe tangential velocity and factors influencing the magnitude of tangential velocity.

Is a product of angular velocity and radius of rotation. Increase can cause big change in tangental velocity. the velocity obtained by differating displacement factors are angular velocity and the radius of circle Linear velocity direction is at a tangent to the curved path. r x w

In a classical study on reaching and pointing, participants were asked to hold a manipulandum and make straight planar movement from the center of the workspace to different targets. The linear and angular kinematics data are presented below. Which of the following interpretations is INCORRECT.

Joint angle velocities show similar profiles when the hand moves from different side of the body. So these are true: Elbow and shower joints show coordinated angular movement to achieve a straight path of the hand. Shoulder joint angle position reverses direction when reaching to a target at the opposite side of the body. Hand velocities show similar profiles when participants reach to different locations.

Describe the key difference between linear and angular motion.

Linear motion is a uniform motion of the system of interest: all parts moving in the same direction at the same speed. It consists of rectilinear and curvilinear. Angular motion is the rotation around a central imaginary line, known as axis of rotation. It is perpendicular to the plane of motion, and passes through the center. It is spinning.

Given an acceleration of -6 m/s2, which of the following statements is always true?

None of the statements are necessarily true: Forward motion is occurring, Backward motion is occurring, Rate of change of position is constant.

Describe what is one gait cycle and major phases of a gait cycle.

One gait cycle is 2 complete steps, which is one stride. Time interval between two identical actions is a gait cycle. One gait cycle is equal to 1 stride. There are two phases the stance phase and the swing phase. The stance phase is the foot on the ground, which is 60% of the time. The swing phase is when the foot is in the air, which is 40% os one cycle time.

A 200-meter swimming race takes place in a 50-meter pool. Assume that the positive direction is the direction of swimming in the first stretch (first 50 m). How will the acceleration of the swimmer be when the swimmer is slowing down to make his second turn, that is, as he approached the 100 m point of the race?

Positive

When one returns to the fundamental position from the anatomical position, which joint in the elbow make this movement?

Proximal radioulnar

Which of the following is an example of angular motion

The arm of a golfer during a golf-swing

In an experiment on patients with Parkinson's disease, patients' gait data were collected, and joint angles over gait cycle were plotted below. Explain what are the major differences between PD patients and normal walking pattern. What would be your main interpretation of the walking deficit of PD patients, and in which way you would recommend them to correct these patterns?

The major differences consist of shuffling gait to decrease their chance of falling, decreased step length, more steps are needed to cover the same amount of ground. PD patients are also creating less force, and have a reduced push off force. Faster cadence, slower velocity , longer stance. reduce ankle plantar flexion & knee flexion & hip extension. all produce less force in push-off phase. I would recommend them to increase their general strength, to be active regularly. Start some weight lifting, and they need to increase the push off velocity. encouraged increase stride length, by opening ankle and hip ROM.

Describe the major movements of the shoulder complex supported by scapula motion.

The major movements with the scapula are abduction and adduction The major movements of the shoulder complex are upward and downward rotation, elevation and depression (shoulder movement up and down), protraction (abduction), retraction (adduction) supports shoulder protraction and retraction, and horizontal flexion and extension. These are all with the support of the scapula.

When two cyclists enter a slippery curve at the same velocity who is at a higher risk of skidding?

The one at the inner loop

During the end of a 100-m race, a runner's acceleration is negative. Which statement accurately interprets this observation?

The runner is slowing down while moving in the positive direction

When the arm is raised to 180° abduction, the scapula undergoes

Upward rotation

Using the table above, calculate the linear (tangential) velocity of the lateral malleolus at frame 2 using the central difference formula.

Vx = 93.7 - 90.8 / 2(1/60) = 2.9/.033 = 87 Vy= 18.6-16.8/2(1/60)=1.8/.033=54 v = squareroot of 87^2 + 54^2 = 102.4

Which of the following stages of right-leg gait cycle occurs first?

We strike our right heel on the ground as the initial contact.

In a classical study on reaching and pointing, participants were asked to hold a manipulandum and make straight planar movement from the center of the workspace to different targets. The linear and angular kinematics data are presented below. Which of the following interpretations is INCORRECT.

When moving to the same target from a different side of the body, shoulder joint's angular velocities show similar profiles.

In a sprinting study, the following graph was obtained. Which of the following interpretation is INCORRECT?

When sprinting at higher speed, runners increase their stride length more than their stride rate.

Celine and John are running around a curve with a radius of 9 m. If Celine's tangential velocity is 6 m/s and John's angular velocity is 1.2 rad/s, _____ experiences a higher centripetal acceleration at ______ m/s2.

ac=v^2 / r John, 12.96 m/s2

For the plot below, the angular acceleration vector would be positive in which region?

c

In the following diagram of lower-limb joint angles, which one is an relative angle of the knee?

d

Sagittal plane motion of the ankle is called

dorsiflexion and plantar flexion

From the following angle data obtained during walking, we know that during the heel off phase (~40% of the gait cycle), the hip ____ and the knee ____.

extends, extends

Which of the following series of human gait cycle stages is in correct chronological order (from earliest to latest)? Note: not all stages will be listed in any series.

heel strike, foot flat, heel rise, midswing, terminal swing

In the absence of any air-drag, skydiving from a stationary helicopter would result in ________ motion whereas skydiving from a moving aircraft would result in ________ motion of the jumper.

rectilinear, curvilinear

Which plane is this movement performed in? (picture)

sagittal

The following figure shows the velocity, and acceleration of motion during a shuttle run. At which time period is the runner moving backwards and slowing down? (picture)

t3 - t4

The following figure shows the knee flexion angle during the gait cycle. Notice that as per the convention adopted by the International Society of Biomechanics (ISB), a straight knee is at 0° flexion. As per that convention, the peak knee flexion (60°) occurs around 80% of the gait cycle (during swing phase). What biomechanical purpose is best served by the large knee flexion?

toe clearance during swing

Which plane is this movement performed in?

transverse