EXSS 385 Exam 2
Newton's 3rd Law of Motion Law of Reaction
- For every action, there is an equal and opposite reaction - When one body exerts a force on a second, the second body exerts a reaction for that is equal in magnitude and opposite in direction of the first body
Absolute angle
- Horizontal reference - Vertical reference angular orientation of a body segment with respect to a *fixed line of reference* Absolute angles should consistently be measured in the same direction from a single reference - either horizontal or vertical.
FRONT formulas
0 = v1 + at d = vit + 1/2at^2 0 = vi^2 + 2ad
Equation for How High?
0 = vf^2 + 2ad
Properties of a Force
1. Push or Pull 2. Causes or tends to cause change in the motion or shape of an object 3. measured in Newtons (N)
Types of Forces
1. Resistive 2. Motive
Steps for solving a projectile problem
1. v = rw 2. set up triangle and find x & y using cos and sin. 3. v = at 4. multiply time by 2 5. d = vt (using v from vx found in step 2)
How much force must be applied by a kicker to give a stationary 2.5 kg ball an acceleration of 40 m/s^2?
100 N
A high jumper with a body weight of 712 N exerts a force of 3 kN against the ground during takeoff. How much force does the ground exert on the high jumper?
3kN because of Newton's Third Law - Law of Rxn: for every action, there is an equal and opposite reaction.
Newton's 1st Law of Motion Law of Inertia
A body will maintain a state of rest or constant velocity unless acted on by an external force that changes the state **a body in motion stays in motion; a body at rest stays at rest; unless acted on by an external force. (Friction and air resistance are two forces normally present that act on body in motion.)
Newton's 2nd Law of Motion Law of Acceleration
A force applied to a body causes an acceleration (of that body) [of a magnitude] proportional to the force, in the direction of the force, and inversely proportional to the body's mass - acceleration is proportional to force (in magnitude) and in the direction of the force - acceleration is inversely proportional to mass T = Ia F = ma - When a ball is thrown, kicked, or struck with an instrument (bat, stick, etc), it tends to travel *in the direction of the line of action of the applied force*. - Similarly, the greater the amount of force applied, the greater the speed the ball has.
Explain how the velocity of the ball in Problem 4 would differ if the stick were swung at a 30° angle to the direction of motion of the horse.
It would decrease because only a component of the velocity is going in the same direction as the horse.
Relative Angle
Anatomical reference position - angle at a joint formed b/ the longitudinal axes of adjacent body segments The convention used for measuring relative joint angles is that in anatomical reference position, all joint angles are at 0 degrees. Relative angles should consistently be measured on the same side of a given joint.
d = r θ v = r ω a = r α
Angular Variables (must be in radians)
The angular velocity of a runner's thigh changes from 3 rad/s to 2.7 rad/s during a 0.5 s time period. What has been the average angular acceleration of the thigh?
Answer: -0.6 rad/s2, -34.4 deg/s^2
**A soccer ball is kicked from the playing field at a 45° angle. If the ball is in the air for 3 s, what is the maximum height achieved?
Answer: 11.025 m d = 1/2at^2 a = 9.81 t = 1.5 s (given)
A tennis ball leaves a racket during the execution of a perfectly horizontal ground stroke with a speed of 22 m/s. If the ball is in the air for 0.7 s, what horizontal distance does it travel?
Answer: 15.4 m d=vt
**A 1.2 m golf club is swung in a planar motion by a right-handed golfer with an arm length of 0.76 m. If the initial velocity of the golf ball is 35 m/s, what was the angular velocity of the left shoulder at the point of ball contact? (Assume that the left arm and the club form a straight line, and that the initial velocity of the ball is the same as the linear velocity of the club head at impact.)
Answer: 17.86 rad/s
A trampolinist springs vertically upward with an initial speed of 9.2 m/s. How high above the trampoline will the trampolinist go?
Answer: 4.31 m Vi = 9.2 m/2 a = -9.81 m/s^2 because going up (against gravity) Vf = 0 Vf^2 = Vi^2 + 2ad
A tennis racquet swung with an angular velocity of 12 rad/s strikes a motionless ball at a distance of 0.5 m from the axis of rotation. What is the linear velocity of the racquet at the point of contact with the ball?
Answer: 6 m/s
**A polo player's arm and stick form a 2.5 m rigid segment. If the arm and stick are swung with an angular speed of 1.0 rad/s as the player's horse gallops at 5 m/s, what is the resultant velocity of a motionless ball that is struck head-on? (Assume that ball velocity is the same as the linear velocity of the end of the stick.)
Answer: 7.5 m/s
A kicker's extended leg is swung for 0.4 s in a counterclockwise direction while accelerating at 200 deg/s^2. What is the angular velocity of the leg at the instant of contact with the ball?
Answer: 80 deg/s, 1.4 rad/s
****A baseball is struck by a bat 46 cm from the axis of rotation when the angular velocity of the bat is 70 rad/s. If the ball is hit at a height of 1.2 m at a 45° angle, will the ball clear a 1.2 m fence 110 m away? (Assume that the initial linear velocity of the ball is the same as the linear velocity of the bat at the point at which it is struck.)
Answer: No, the ball will fall through a height of 1.2 m at a distance of 105.7 m.
Goniometer
One arm fixed to protractor at 0 deg Other arm free to rotate Center of goniometer over joint center Arms aligned over longitudinal axes - commonly used by clinicians for direct measurement of relative joint angles on a human subject.
A pitched ball with a mass of 1 kg reaches a catcher's glove traveling at a velocity of 28 m/s. a. How much momentum does the ball have? b. How much impulse is required to stop the ball? c. If the ball is in contact with the catcher's glove for 0.5 s during the catch, how much average force is applied by the glove?
a. 28 kg * m/s b. 28 N s c. 56 N UNITS **** Momentum = kg * m/s Impulse = N*s
A soccer ball is kicked with an initial horizontal speed of 5 m/s and an initial vertical speed of 3 m/s. Assuming that projection and landing heights are the same and neglecting air resistance, identify the follow- ing quantities: a. The ball's horizontal speed 0.5 s into its flight b. The ball's horizontal speed midway through its flight c. The ball's horizontal speed immediately before contact with the ground d. The ball's vertical speed at the apex of the flight e. The ball's vertical speed midway through its flight f. The ball's vertical speed immediately before contact with the ground
a. horizont. speed = 5 m/s because horizontal velocity of a projectile is CONSTANT b. horizont. speed = 5 m/s because horizontal velocity of a projectile is CONSTANT c. horizont. speed = 5 m/s because horizontal velocity of a projectile is CONSTANT d. speed = 0 m/s at the apex of the flight because the ball changes directions at the apex and must STOP at that point (apex) in order to change directions. e. vert speed = 3 m/s because take-off and landing heights are the same; therefore, takeoff and landing speeds are the same
The relative angle at the knee changes from 0° to 85° during the knee flexion phase of a squat exercise. If 10 complete squats are performed, what is the total angular distance and the total angular displacement undergone at the knee?
angular distance = 1700°, 29.7 rad angular displacement = 0 The angular displacement is 0 because the start and finish positions of the knee are the same (0 degrees). Therefore, final position - initial position = 0.
**An archery arrow is shot with a speed of 45 m/s at an angle of 10°. How far horizontally can the arrow travel before hitting a target at the same height from which it was released?
d = 70.6 m
Equation for How Far?
d = v1*t d = vt
Equations for constant acceleration so a = 0
d = vt vf = vi
clockwise
negative
counterclockwise
positive
Select one sport or daily activity, and identify the ways in which the amount of friction present between surfaces in contact affects performance outcome.
the amount of friction between two surfaces can be changed by altering the coefficient of friction between the surfaces. For example, the use of batting gloves in softball increases the coefficient of friction between the hand and the grip of the bat. Other examples: - gloves for golf - gloves for wide receivers in football
Identify the angular displacement, the angular velocity, and the angular acceleration of the second hand on a clock over the time interval in which it moves from the number 12 to the number 6. Provide answers in both degrees and radian-based units.
the movement is clockwise so..... angular displacement = -180 deg; -π rad angular velocity (deg/s) = -6 deg/s; -.105 rad/s ω = Δθ / t = -180 deg/30 s = -6 deg/s -6 (π / 180) = -.105 rad/s or -π /30 rad/s (t = 30 seconds because going from 12 to 6 on the clock) angular acceleration α = ω / t = 0 / 30 s (0 b/c velocity is constant)
**Two skaters gliding on ice run into each other head-on. If the two skaters hold onto each other and continue to move as a unit after the collision, what will be their resultant velocity? Skater A has a velocity of 5 m/s and a mass of 65 kg. Skater B has a velocity of 6 m/s and a mass of 60 kg.
v = -.028 m/s Left or backward; So they will continue gliding in the direction originally taken by skater B use: m1v1 + m2v2 = (m1 + m2) v and F = ma
Lineman A has a mass of 100 kg and is traveling with a velocity of 4 m/s when he collides head-on with lineman B, who has a mass of 90 kg and is traveling at 4.5 m/s. If both players remain on their feet, what will happen?
v = -.03 m/s Left or backward lineman B will push lineman A backward with a velocity of .03 m/s use: m1v1 + m2v2 = (m1 + m2) v
BACK half of parabolic pathway Formulas
v2 = at d = 1/2at^2 v2^2 = 2ad
***A badminton shuttlecock is struck by a racket at a 35° angle, giving it an initial speed of 10 m/s. How high will it go? How far will it travel horizontally before being contacted by the opponent's racket at the same height from which it was projected?
vert d = 1.68 m t = 1.17 s horizont d = 9.58 m