Mechanical Analysis Exam 2
Plane
smooth flat space defined by two axes.
any motion in this space is called planar
our world is three dimensional
true
resultant
a vector that is equivalent to the combine effect of two or more vectors
component
parts of a resultant vector; two or more vectors that are acting in different directions
(typically the x and y components)
when a vector is not parallel to an axis you must what?
correct for it
what acts as the correction factor?
sine/cosine
the magnitudes of the x and y components will be equal to what?
45 degrees
The magnitude of the resultant vector is always larger than the two components, or
equal to one of the components if the other component is zero.
true
If the angle is greater than 45 deg, the Y component will be greater than the X
component.
true
If the angle is less than 45 degrees, the X component will be greater than the Y
component.
true
A skateboarder takes off a ramp, what determines how high and how far he will go?
takeoff velocity
takeoff angle
takeoff height
projectile
Any airborne body that is only subjected to gravity and wind resistance after it has left the
ground
trajectory
path of projectile, a parabola
gravity
Acceleration of a body due to the force of gravity
on earth gravity is
Constant
Acting downward (negative)
-9.81 m/s2
the velocity due to gravity is not constant
true
,If the same person jumps off a 3 m platform with the same velocity (6 m/s), we will see
different trajectories:
They would travel a greater horizontal distance from the higher platform due to a longer
time in the air.
Even though they started more than 3 times higher, they only landed around 2 times further.
For a Projectile Leaving and Landing at Same Height: 4 step process
Solve for the x and y components of velocity
Solve for total time the projectile is in the air
Solve for horizontal displacement (range of the projectile)
Solve for vertical displacement (max height of the projectile from the ground to the apex)
A ______ vector is the combine effect of two or more vectors
resultant
If the x component of velocity is 7 m/s, and the y component of velocity is 9 m/s, what
is the resultant velocity?
11.4 m/s
If a ball is kicked at an angle of 60 degrees, which of the following statements is true?
Both the x and y components of velocity are equal
The y component of velocity is greater than the x component of velocity
The x component of velocity is greater than the y component of velocity
The y component of velocity is greater than the x component of velocity
What is the vertical velocity at the apex of the trajectory?
0
What happens to the projectile's vertical velocity as it moves from the ground to the
apex? What happens to the projectile's vertical velocity as it moves from the apex to
the ground?
It decreases as it moves up, and increases as it moves down.
What happens to the projectile's horizontal velocity as it moves from the ground to the
apex? What happens to the projectile's horizontal velocity as it moves from the apex
to the ground?
It stays constant.
acceleration equations will be on the test
you still have to know how to use them tho
parabola
type of plane curve the trajectory of the projectile
apex
highest point of a trajectory
relative height
difference between the vertical position at takeoff and the vertical position at landing
range
horizontal displacement of a projectile
Sam: American football placekicker: he's having trouble making a field goal from the
40 yd line because the kick is too short; really a 57 yd kick bc your 7 yds back from the
line of scrimmage and 10 yds from the goal line. The takeoff angle of his kicked ball is
36 degrees and take off velocity is 76 ft/sec. How does he fix this?
, he needs to focus on increasing his velocity and applying more force to the ball
Monica is a HS basketball player who had ACL surgery 6 months ago. She has
concerns about the cutting maneuver. How can we help her?
encourage her to do smaller angle cuts, gradually increase her cuts and speed as she
recovers and gets stronger
What is the magnitude of the acceleration of a projectile due to gravity? In what
direction will this acceleration be in?
-9.81 m/s 2. Downward
Once the projectile is in the air, what is the acceleration of a projectile in the
horizontal (x) direction? What is the object's velocity in the horizontal direction?
0 m/s, velocity in the horizontal direction is constant
What is the relationship between the time it takes a projectile to go from the ground to
the apex and the time it takes the projectile to go from the apex back to the ground, if
the take-off and landing heights are the same?
The time it takes to go up is the same time in takes to go down.
Consider a patient you are working with that is using a manual wheelchair. Is the
motion of the wheel the same as they motion of a body previously explored? What can
we do to help them rotate the wheels more efficiently?
not the same; we can help them strengthen their arm and increase the angle of where their
arm is to have more force behind it
Rigid Body
body that maintains a constant shape
example of a rigid body
baseball bat
what would be a good example of a rigid body in the human body?
bone; specifically long bones are better because they are designed to rotate quickly
axis of rotation
a fixed line about which a body rotates
Frame of reference and axis of rotation
rotations occur in a plane about an axis
z-axis
anterior/posterior axis = rotation in the xy plane (frontal)
y-axis
polar axis = rotaiton in the xz plane (transverse)
x-axis
medial/lateral axis= rotation in the yz plane (saggital)
clockwise rotations are what?
negative
counterclockwise rotations are what?
positive
angular position (theta)
the orientation of a rigid body in reference to some axis
what can angular position be measured in?
degrees and radians
Plane
smooth flat space defined by two axes.
any motion in this space is called planar
our world is three dimensional
true
resultant
a vector that is equivalent to the combine effect of two or more vectors
component
parts of a resultant vector; two or more vectors that are acting in different directions
(typically the x and y components)
when a vector is not parallel to an axis you must what?
correct for it
what acts as the correction factor?
sine/cosine
the magnitudes of the x and y components will be equal to what?
45 degrees
The magnitude of the resultant vector is always larger than the two components, or
equal to one of the components if the other component is zero.
true
If the angle is greater than 45 deg, the Y component will be greater than the X
component.
true
If the angle is less than 45 degrees, the X component will be greater than the Y
component.
true
A skateboarder takes off a ramp, what determines how high and how far he will go?
takeoff velocity
takeoff angle
takeoff height
projectile
Any airborne body that is only subjected to gravity and wind resistance after it has left the
ground
trajectory
path of projectile, a parabola
gravity
Acceleration of a body due to the force of gravity
on earth gravity is
Constant
Acting downward (negative)
-9.81 m/s2
the velocity due to gravity is not constant
true
,If the same person jumps off a 3 m platform with the same velocity (6 m/s), we will see
different trajectories:
They would travel a greater horizontal distance from the higher platform due to a longer
time in the air.
Even though they started more than 3 times higher, they only landed around 2 times further.
For a Projectile Leaving and Landing at Same Height: 4 step process
Solve for the x and y components of velocity
Solve for total time the projectile is in the air
Solve for horizontal displacement (range of the projectile)
Solve for vertical displacement (max height of the projectile from the ground to the apex)
A ______ vector is the combine effect of two or more vectors
resultant
If the x component of velocity is 7 m/s, and the y component of velocity is 9 m/s, what
is the resultant velocity?
11.4 m/s
If a ball is kicked at an angle of 60 degrees, which of the following statements is true?
Both the x and y components of velocity are equal
The y component of velocity is greater than the x component of velocity
The x component of velocity is greater than the y component of velocity
The y component of velocity is greater than the x component of velocity
What is the vertical velocity at the apex of the trajectory?
0
What happens to the projectile's vertical velocity as it moves from the ground to the
apex? What happens to the projectile's vertical velocity as it moves from the apex to
the ground?
It decreases as it moves up, and increases as it moves down.
What happens to the projectile's horizontal velocity as it moves from the ground to the
apex? What happens to the projectile's horizontal velocity as it moves from the apex
to the ground?
It stays constant.
acceleration equations will be on the test
you still have to know how to use them tho
parabola
type of plane curve the trajectory of the projectile
apex
highest point of a trajectory
relative height
difference between the vertical position at takeoff and the vertical position at landing
range
horizontal displacement of a projectile
Sam: American football placekicker: he's having trouble making a field goal from the
40 yd line because the kick is too short; really a 57 yd kick bc your 7 yds back from the
line of scrimmage and 10 yds from the goal line. The takeoff angle of his kicked ball is
36 degrees and take off velocity is 76 ft/sec. How does he fix this?
, he needs to focus on increasing his velocity and applying more force to the ball
Monica is a HS basketball player who had ACL surgery 6 months ago. She has
concerns about the cutting maneuver. How can we help her?
encourage her to do smaller angle cuts, gradually increase her cuts and speed as she
recovers and gets stronger
What is the magnitude of the acceleration of a projectile due to gravity? In what
direction will this acceleration be in?
-9.81 m/s 2. Downward
Once the projectile is in the air, what is the acceleration of a projectile in the
horizontal (x) direction? What is the object's velocity in the horizontal direction?
0 m/s, velocity in the horizontal direction is constant
What is the relationship between the time it takes a projectile to go from the ground to
the apex and the time it takes the projectile to go from the apex back to the ground, if
the take-off and landing heights are the same?
The time it takes to go up is the same time in takes to go down.
Consider a patient you are working with that is using a manual wheelchair. Is the
motion of the wheel the same as they motion of a body previously explored? What can
we do to help them rotate the wheels more efficiently?
not the same; we can help them strengthen their arm and increase the angle of where their
arm is to have more force behind it
Rigid Body
body that maintains a constant shape
example of a rigid body
baseball bat
what would be a good example of a rigid body in the human body?
bone; specifically long bones are better because they are designed to rotate quickly
axis of rotation
a fixed line about which a body rotates
Frame of reference and axis of rotation
rotations occur in a plane about an axis
z-axis
anterior/posterior axis = rotation in the xy plane (frontal)
y-axis
polar axis = rotaiton in the xz plane (transverse)
x-axis
medial/lateral axis= rotation in the yz plane (saggital)
clockwise rotations are what?
negative
counterclockwise rotations are what?
positive
angular position (theta)
the orientation of a rigid body in reference to some axis
what can angular position be measured in?
degrees and radians
