Midterm 2 Flashcards
Get that A-ss
What Kind of Path does an object follow via Projectile Motion
A Parabolic Path with Uniform Acceleration
Apex
The Peak of the Parabala (@ which point vertical velocity = 0)
- The highest point achieved
- Occurs at ½ the total flight time
5 Factors that Effect Projectile Motion
- Velocity at Takeoff
- Relative Height at Takeoff
- Air Resistance
- Acceleration Due to Gravity
- Angle of Release
Describe the flight path of a ball using projectile motion principles
- Lets look at the horizontal component (x) at different points along the Parabolic path. From Newton’s 1st law we know that an object’s state of motion will remain the same unless an external force acts on it. If we neglect any air resistance, then the horizontal component of the velocity will remain unchanged throughout the flight. (ie, the object will not slow down or speed up, horizontally)
- Lets look at the vertical component (y) at different points along the parabolic path. We know that there is a constant non-contact force acting vertically on the object. The force of gravity. Therefore there is a constant acceleration downward. This acceleration is 9.81 m/s2. Said in other words the vertical velocity of the object will change 9.81 m/s for every second.
- Because the acceleration is downward facing and the velocity is upward facing the velocity will decrease 9.81 m/s for every second. At the first point along our path the vertical velocity will be smaller than it was originally.
- Something very important happens at our next point on the parabolic path of the object. This point is called the apex because it is the peak of the parabola. At this point the downward acceleration of gravity has decreased the vertical velocity to zero. The apex is a very important point and we will revisit this later.
- At the next point on our parabolic path. The downward acceleration of gravity has caused our object to have a negative vertical velocity.
- When the object comes back to land on the ground the vertical velocity is downward. If it lands at the same height that it took off It will have the same magnitude of the initial vertical velocity but acting in the opposite direction.
What Effects Velocity @ Take-off of Projectile Motion?
take-off velocity is a result of the momentum
of the object and the momentum of the
object is a result of the impulse imparted to it
Why does mass not effect projectile motion?
When an object is in free fall it experiences the same acceleration due to gravity as a lighter object or a heavier object. (recall NASA bowling ball / feather)
-Momentum is still effected
What effects Angle of Release ( Projectile Motion_
The angle of release is determined by the direction of the velocity vector at
Take-off which is determined by the direction of the force vector. We can
Directly control the angle of release through force application
- Optimal for height = 90 degrees up
- Optimal for distance = 45 degrees
Speed vs Take-Off relationship
Faster horizontal speed results in shallower take-off angle
Optimal take-off angle
for long jump is 15-27°
Factors effecting Relative Height at Take-Off
The relative height at take-off can be effected by changing the levels of the take-off and landing surfaces or changing the position of an individuals center of gravity
Factors effecting Air Resistance
Air resistance can only be changed by the surface and shape of the object
Factors effecting Acceleration d/t Gravity
The acceleration due to gravity can only be changed by your position relative to the earth’s core
A Lever
- Is a rigid object that is attached to a fulcrum or pivot point
- Can be used to multiply the mechanical force that can be applied to another object.
-A force can be applied (almost) anywhere on the
rigid object and will tend to cause rotation of the
rigid body about the fulcrum
Torque ( think of the doors)
• it is the result of a force (F) applied a certain perpendicular distance (dp) from
an axis of rotation.
T = Fdp = dependent on size and place of the force
Is a tendency for an object to rotate about an axis caused by a force.
- is also called moment of force or simply moment.
- Think of torque as a rotary force.
- Even if an object doesn’t move a torque may be present
Influences of Torque
- Line of Action of the Force
- The Acting Forces Magnitude
- Point of Action on the Lever
Axis of Rotation
• The axis of rotation can be fixed.
- the hinges on a door
- your forearm is fixed to your elbow axis
or
• the axis of rotation can be free.
- An example of this is when dealing with the axis of
rotation of your whole body
Why a Lever is good
A lever can be used to multiply the mechanical force that can be applied to another object.
Force Arm
The perpendicular distance from the line of action of the applied force and the fulcrum is called the force arm (FA)
Resistance Arm
The perpendicular distance from the line of action of the object force and the fulcrum is called the resistance arm (RA) because the object is resisting the applied force
An example of Mechanical advantage with a Lever
Less force is needed to hold the object up if the
force is applied further from the fulcrum
• This is how a lever can be shown to create a mechanical
advantage
• The decrease in magnitude of force is directly proportional to the distance that the force was moved away from the fulcrum
Vice Versa,
• More force is needed to hold the object up if the force is
applied closer to the fulcrum
• This is because torque is dependent on the magnitude of the
force and where the force is applied
Moment Arm
The perpendicular distance (90 degrees) from the line of action of the force to the axis of rotation which the torque is dependent on
First Class Lever
The applied force and resistance arm are on either sides of the fulcrum
ex) Teeter-totter Oars on a boat Catapult Shoehorn Scissors Pair of pliers
Second Class Lever
• The applied force and the resistance
are on the same sides of the fulcrum
• The force is farther from the fulcrum
than the resistance
ex)
Wheelbarrow
Crowbar
Nut cracker
Third Class Lever
• The applied force and the resistance
are on the same sides of the fulcrum
• The force is closer to the fulcrum
than the resistance
ex) Tweezers Stapler Mousetrap Broom Hockey stick biceps brachii
Torque and Bicycle Gears
low gear vs High gear
A low gear (smaller ratio of front to rear gear) results in greater force
transmitted to the ground over a smaller distance
A high gear (larger ratio of front to rear gear) results in lesser force
transmitted to the ground over a greater distance
Levers and Muscular Force
The movement of limb segments is caused by muscular contraction (force) attached a distance away from a joint (axis of rotation)
Might not seem like a mechanical advantage but
a small displacement closer to the axis causes a much greater displacement farther away from the axis
• So the muscle must only shorten a little to move something at the hand a lot
What would happen if you applied the force through the axis of rotation?
If the line of action of the force
passes through the axis of rotation
there is no perpendicular distance
and therefore no moment arm
• There is no moment arm so there
would be no torque
Positive vs Negative Torque
Clockwise rotation = -ive
Counterclockwise rotation = +ive rotation
Can we add torque?
Yes if it is acting around the same axis, since it’s a vector quantity we can add that shit
Static Equilibrium
Not only must the forces be zero for a system to be
in static equilibrium but the torques must also be
zero.
The Net Torque will decide which way the object rotates
How do different bar positions in the squat effect torque?
In an upright squat (hips are less flexed = upright posture) the load is distributed equally between the hip and knee because the moments are equal. However, one is likely to experience greater knee extensor challenge than hip extensor challenge because the torque producing capabilities at the two joints are not equal, i.e. typically hip extensor strength is greater than knee extensor strength.
In a front squat (bar in front) load position has influenced body position in such a manner that a larger moment of resistance is created at the knee, which is often why it is stated in lay terms that “front squats emphasize quads”.
In a regular squat hips are more flexed = angled a larger moment is created at the hips (and lumbar spine). It is likely that this individual will experience squats as primarily a “butt and low back exercise” because that is exactly what is being challenged due to the moments of resistance. Fatigue/failure in the low back is likely to preclude any noticeable challenge to the quadriceps.
Why is it important to keep the bar close during a deadlift
to keep the moment arm perpindicular to the axis of rotation (the hip) this makes the bar easier to move as it increases the torque sine increased moment arm = increased torque
the longer the moment arm, the more torque applied to the point of rotation, therefore the greater the effect of gravity and the stronger our hip extension has to be.
Vice Versa, we bring the bar in to decrease the moment arm, thus decreasing the torque making the bar easier to move.
With a Sumo deadlift, we effectively reduce the moment arm, by squeezing the hips close to the bar and maintaining a synergistic movement at the shoulder and hips (both move up as you squeeze the hips forward)
Torque in a Baseball Pitch
Movement about certain joints can cause movement about other joints
• This is made possible through the concept of kinetic linking
There is rotation in the shoulders assisted by the rotation at the hips
• More torque about the vertical axis
•There is rotation of the upper arm about the shoulder and the forearm about the elbow in the sagittal/transverse plane.
• The coordinated action of the whole movement transferring the torques and forces across joints is an example of kinetic linking
Torque in golf
1. The forces at the feet will cause a rotational torque that is transferred from feet to hips…. 2. Our feet may remain stationary but our hips may rotate This may also cause a rotation of Our shoulders 3. The rotation of our shoulders will Cause a movement of our arm Which will result in a force on the handle
Toque about a Free Axis
So a force through the center tends to cause a change in the linear motion of an object and a force not through the center
tends to cause a change in the angular and linear motion of an object.
• This is because an object will have a tendency to rotate about its center of gravity (balance point)
How to Cause Something to Rotate w/ Torque
Top-Spin of a ball= hit above center of a ball
Backspin = hit below the center of a ball
Or Hit on axis of rotation to cause no rotation
In diving --A force more straight back will cause the diver to rotate counter clockwise --A force more up and down will cause the diver to rotate clockwise
A force directed through the
center of the diver will allow the
diver to maintain her orientation
Why is it easier to hold weight with extended arms?
because Movement of a limb can cause a change in the orientation of the muscle force vector relative to the limb, thereby changing the moment arm.
= if all in a line, there is no perpendicular moment, = no moment arm = no torque.
Center of Mass
The average location of all of the mass in a body.
When does the Center of Mass = Center of Gravity?
Centre of Mass = Centre of gravity
• When the object is close to the earth
Center of Gravity
the point in a body or system around which its mass or weight is evenly distributed or balanced and through which the force of gravity acts.
In humans just above the navel region (belly button)
but changes whenever a limb moves (For each limb movement, the center of gravity of the entire body shifts slightly in the direction of that movement.)
- Can also lay outside the body
How to locate the center of gravity
If you attempt to balance an object. The axis or fulcrum
must pass through the center of gravity. If not it will fall
by hanging an object from a few points.
Why does a pencil fall over when you hold it unbalanced
If the axis (fulcrum) is not in line with the center of gravity then the sum of the torques about that point is not balanced and there will be a tendency for rotation
Explain the concept of Hang-Time
The manipulation of the center of gravity by raising your arms and legs when you jump to give the body a floating effect (ushijiima haikyuu)
Stability
A Resistance to move or thrown off balance
Changed by
• Base of support
• Position of CofG
Factors the Effect Stability
Height of center of gravity
• Base of support
• The weight of the object
Base of Support
is the area within the lines connecting the outer perimeter of each of the points of support.
• A large base of support provides great stability
because there is greater area over which to keep
the body weight.
• Conversely a small base of support maximizes
mobility yet requires very good balance
Righting Moment
a torque that tends to return the block to it’s original
position produced by CoG
Toppling Moment
CoG past edge which thus makes the torque produced by the CoG a toppling moment = tendency to fall over
Why will a block with a lower CoG topple further and return to its starting position than a block with a higher CoG
Because when the CoG of the block is lower the moment arm is larger, therefore there is a greater righting moment torque acting upon the object
Balance
a persons ability to control their body
position (CofG) relative to some base of support
Mobility
Ease of movement
Stability Mobility Relationship
Stability and Mobility are inversely related. As stability goes up mobility goes down
Stability / Base of Support Relationship
Horizontal position of CofG from edge of base of support determines how far the weight must be shifted to destabilize someone.
The vertical position of the CofG
- If high it is easy to move outside the base of support
- f low it is difficult to move outside the base of support
Ready Position
Feet Shoulder width apart
Forward and backward mobility
Staggered footwork or square
( varies by sport, think sprint start = super off balance to create biggest topple moment)
Angular Kinematics
The study of motion of an object about a circular path exclusive of the influences of mass and force.
Angular motion occurs when all points on an object move in a circular path around the same axis.
Components of Angular Kinematics
It includes angular displacement, angular velocity, and angular acceleration.
Angular Displacement
Is a Vector arc length (l) = θ x r Magnitude = Degrees/Radians Direction = Positive (counter clockwise rotation) Negative (clockwise rotation)
• The angular displacement of an object is defined as the angle (θ) that it moves through from starting position relative to an axis of rotation
- Theta (θ) is used to represent the angle in many cases
- There are 360 degrees in a full rotation around an axis.
• The angular displacement of an object measured anywhere along the length of the object is always the same
Relative vs Absolute Angular position
- Relative angular position is the position of an object relative to a plane or line that is capable of moving.
- Absolute angular position is the position of an object relative to a fixed reference.
Advantage of muscles when generating angular motion
An advantage of muscle insertions
close to joints is that the muscle only
has to shorten a short distance to
produce a large movement
An advantage of muscle insertions close to joints is that the muscle only has to shorten at a slow velocity to produce a large linear velocity at the end of the limb.
Angular Velocity
• Angular velocity is the rate of change of angular
displacement.
Units = (degrees/second)
w = Delta θ/Delta Time
is typically less than linear velocity.
• the velocity of an object is determined by the displacement of the object and the time that it took the object to move or • The time an object is moving is determined by the velocity of the object and how far it must travel or • The displacement of an object is determined by the velocity of the object and the time it must travel
Tangential Velocity
VT = w(angular velocity) X r
The instantaneous linear velocity of a point on a rotating object is equal to the instantaneous angular velocity of the rotating object times the radius.
• The direction of this velocity is a straight line that is tangent to the circular path
Relationship between Angular and Linear Velocity
Since both share the r (radius) component in their formula we can change both by manipulating the size of the radius or length of rotation
Angular Acceleration
Angular Acceleration = change in Angular Velocity
= omega/ change in Time = T = degrees / second squared
• Angular acceleration occurs when something spins faster or slower than it was.
the point at a farther radial distance would experience a greater change in velocity and therefore a greater linear acceleration
Tangential Acceleration
• The component of linear acceleration tangent to the circular path of a point on a rotating object is called the tangential acceleration.
• The equation for tangential acceleration is
aT = alpha x r
• This shows that the radius is still important in determining the effective linear kinematic quantity.
Centripetal Acceleration
If something is turning around a circle then it required an external force or acceleration to cause it to change direction. (Newton’s 1st Law)
• Ar = w2 X r
• This acceleration is called
centripetal (center seeking)
(spinning a sling)
• Think about running around a curved path. When you run around a curved path you exert a centre fleeing force (centrifugal) but experience a centripetal acceleration (centre seeking)
• In order to maintain an object traveling at an angular
velocity (w) in a circular path at a certain radial distance
(r) , an inward acceleration of Ar is required
