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Gravity
Key Concepts:
Terms in this set (84)
A toy car is moving in a straight line while its speed is decreasing. What is the sign of its acceleration?
The sign cannot be determined without more information.
A cart on a track is moving to the left. The cart is being pushed by an air current so that its speed is increasing as it moves to the left. Which of the following are the correct signs of the velocity v and acceleration a of the cart? Consider the right to be the positive direction.
v a
I. positive positive
II. positive negative
III. negative positive
IV. negative negative
IV.
The acceleration of an object is in the positive x-direction at a particular instant. Based on this information, which one of the following statements about the object's motion must be true?
The object's velocity is changing, but it is unknown whether its speed is increasing or decreasing.
A ball is rolling on a surface in a straight line. It has an acceleration that is in the opposite direction of its velocity. Based on this information, which one of the following statements about the ball's motion must be true?
The ball's speed is decreasing.
A car moves in a straight line with increasing speed. Based on this information, choose the best statement below which describes what must be true about the signs of the car's velocity and acceleration.
The car's velocity and acceleration must both have the same sign.
You toss a marble straight upward. When the marble reaches its maximum height, what is the direction of its acceleration?
downward
in the video vignette you watched above, a cart was pushed up an inclined track, with a toy passenger riding on the cart. Consider the case where the cart's brake was turned on. Which of the following choices best describes and explains the motion of the toy passenger at the maximum height of the cart?
The toy passenger slowed down with the cart on the way up, reached the maximum height with the cart, but then moved down the slope without the cart because an unbalanced force acted on the passenger. The toy passenger experienced the same downward acceleration throughout its entire motion.
In the video above, when you clicked on the center of the ball to track its horizontal (x-direction) motion, what did you notice about the separation between the vertical lines?
The separation between successive lines was about equal.
When you clicked on the center of the ball to track its vertical (y-direction) motion, what did you notice about the separation between the horizontal segments?
The separation between successive segments first decreased and then increased with time.
Based on your measurements, which of the following statements are true about the distance the ball travels in successive equal time intervals?
I) The horizontal distance the ball moves in successive equal time interval stays the same.
II) The vertical distance the ball moves in successive equal time intervals stays the same.
Statement I is true.
Based on your measurements, which of the following statements are true about the ball's velocity?
I) The horizontal component of the ball's velocity is constant.
II) The vertical component of the ball's velocity is constant.
Statement I is true.
Based on your measurements, which of the following statements are true about the ball's acceleration?
I) The horizontal component of the ball's acceleration is zero.
II) The vertical component of the ball's acceleration is zero.
Statement I is true.
SI units used in physics
mass: kg
length: m
time: s
cartesian coordinate system
standard rectangular coordinate system
plane polar coordinate system
uses (r, angle)
angle is positive when ______
measured counterclockwise from ref line
angle is negative when ______
measured clockwise from the ref line
scalar
-described by a single #
- gives magnitude or size
- temp, volume, speed, mass
vector
- has magnitude and direction
- velocity, displacement, acceleration, force
adding vectors
- must have same units
- "tip to tail"
commutative law of vectors
order in which vectors are added is NOT important
negative of a vector
same magnitude but different direction
subtracting vectors
A - B ~> same as A + (-B)
scalar multiplier
3(A + B + c)
multiplying/dividing a vector by a scalar results in a
vector
displacement
change in X or Y (final - initial)
Average speed
path length/elapsed time
average velocity
displacement/time
instantaneous velocity
the limit of the avg velocity as th time interval becomes infinitesimally small
- is = to slope of line tangent to curve of position v time graph
average acceleration
change in velocity/change in time
object is speeding up when .....
signs of acceleration and velocity are the same (both pos or both neg)
object is slowing down when ....
signs of acceleration and velocity are opposite (one pos and one neg)
free falling object
falling under the influence of gravity (g) alone
kinematic equations
Vf= Vi + at
Displacement = Vit + 1/2 a (t)^2
Vf^2 = Vi^2 + (2a)(displacement)
Displacement = 1/2(Vi + Vf)t
Newtons 1st Law
An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net external force.
Newton's Second Law
Sum of external vector forces acting on an object is = to its mass x acceleration
* F = ma
Newton's Third Law
For every action there is an equal and opposite reaction
2F = -2F
Fg =
mg
normal force =
N
~ is perpendicular
~ is an elastic force that arises from the cohesion of matter and is electromagnetic in origin
~ is NOT the reaction force to gravity
Tension force =
T
Spring force
Fspring = -kx
(k - spring constant)
static friction
Fs ≤ usN
- object does not move unless the force exceeds some critical value
- this critical value is known as maximum static friction force
uk < us
kinetic friction
Fk = ukN
- arises during motion
- the larger the normal force, the larger the kinetic friction is
Based on Newton's first law, what can you say about the motion of the dry ice puck and the net force on it?
The net force on the dry ice puck was essentially zero. This is why it continued in a straight line at a constant speed until it was caught.
What did your velocity vs. time graph for the dry ice puck indicate about its acceleration?
The acceleration was essentially zero.
Using Newton's second law and the velocity vs. time graph for the rocket cart, what can you conclude about the net force on the rocket cart from the time when it was first released to just before it was caught by the rope?
The net force on the cart was approximately constant but not zero.
The second time you created a velocity vs. time graph, the fan cart had twice the mass as in the initial run. Which of the following is true about the acceleration of the fan cart which had double the mass?
The acceleration of the fan cart was approximately half as much as it was for the first run.
Consider two objects, where the second object is twice as massive as the first. The same net force acts on each object. Based on Newton's second law, which of the following is true about the acceleration of the two objects?
The second, more massive object will have half the acceleration as the first object.
The first collision shown in the video is one between two identical carts moving at the same speed. The forces that each cart exerts on the other during the collision is plotted. What does the plot of the forces indicate?
The forces that the carts exert on each other during the collision have the same magnitude but opposite directions.
a collision between a cart with a large mass and one with a small mass is shown. Again, the forces during the collision are plotted. What does the plot of the forces indicate in this case?
The forces that the carts exert on each other during the collision have the same magnitude but opposite directions.
The collision between the lighter and heavier carts is shown again with a small toy figure riding on each cart. Which of the following statements is true about the different effects on the toy figures during the collision?
The force each cart exerts on the other has the same magnitude. However, the lighter cart has a lower mass than the heavier cart, and therefore, according to Newton's second law, it has a greater acceleration than the heavier cart.
As a block slides down a frictionless incline, which of the following statements is true?
Its speed increases and its acceleration remains constant.
If an object is in equilibrium, which of the following statements is NOT true?
The object must be at rest.
- equilibrium means the object is either at rest or is moving at a constant velocity (in both cases a = 0)
A truck loaded with sand accelerates along a highway. The driving force on the truck remains constant. What happens to the acceleration of the truck as its trailer leaks sand at a constant rate through a hole in its bottom?
It increases at a steady rate
A large crate of mass m is placed on the back of a truck but not tied down. As the truck accelerates forward with an acceleration a, the crate remains at rest relative to the truck. What force causes the crate to accelerate forward?
the force of friction between the crate and the floor of the truck
Which of the following statements are true?
An astronaut's weight is the same on the Moon as on Earth.
An astronaut's mass is the same on the International Space Station as it is on Earth.
Earth's gravity has no effect on astronauts inside the International Space Station.
An astronaut's mass is greater on Earth than on the Moon.
None of these statements are true.
An astronaut's mass is the same on the International Space Station as it is on Earth.
A woman is standing on the Earth. In terms of magnitude, her gravitational force on the Earth is which of the following?
equal to the Earth's gravitational force on her
contact forces
result from physical contact between two objects
field forces
Act on objects separated by distance
- "invisible" influence
ex: nuclear forces between subatomic particles, electronegative forces, gravity
- classical physics deals only w/ gravity and electromagnetic forces because they have infinite range
inertia
the tendency of an object to continue its original state of motion
inertial mass
measure of the objects resistance to change in motion due to a force
Newton is equal to
kg*m/s^2
gravitational force
mutual force of attraction;) between any 2 objects in the universe
Newton's Law of Universal Gravitation
The law that says every object in the universe attracts every other object with a force that is directly proportional to the product of masses of the particles and inversely proportional to the square of the distance between them. (the greater the mass of an object, the greater the attraction; the farther apart the objects, the weaker the attraction)
Newton's Law of Universal Gravitation equation
Fg=G(m1m2/r^2)
~ G = universal gravitation constant and is equal to 6.67x10⁻¹¹ N×m²/kg²
weight
magnitude of gravitational force acting on an object
~ w = mg
2 forces in an action - reaction pair always __________
*act on different objects
(book pushes down on TABLE & table pushes up on BOOK) ^ see how the object that receives the force is different
free body diagrams include only ________
forces acting directly on the object in question
case #1 of normal force problems: normal force on a level surface
n - mg = 0
n = mg
case #2 of normal force problems: normal force on a level surface with an applied force
n + Fa(sinθ) - mg = 0
n = mg - Fa(Sinθ)
if θ of applied force is positive, normal force is smaller (N = mg - Fa(Sinθ))
if θ of applied force is negative, normal force is larger because it has to equal mg plus the applied force (N = mg + Fa(Sinθ))
case #3 of normal force problems: normal force on a level surface with acceleration
acceleration increases the magnitude of the normal force
n - mg = may
n = mg + may
case #4 of normal force problems: normal force on a slope
step 1) make axis align with slope so that x axis is the slope
step 2) make gravity into x and y components
n - mg(cosθ) = 0
n = mg(cosθ)
normal force & atmospheric pressure (not really important)
- n force also opposes the downward pressure of the atmosphere
- in problems it will be assumed that pressure forces on objects cancel
tension force exerts force on ________
both the object and the person/thing exerting the force on the cable
case #1 of tension problems: vertical tension forces on a static object (weight hanging from a cable)
a = 0 bc object is static
T - mg = 0
T = mg
case #2 of tension problems: vertical tension forces on acceleration objects (elevator problem)
T - mg = may
T = may + mg
(^ can rearrange to T = m(ay +g)
positive acceleration increases T (ex: T = 2(5+9.81)... T = 29.62
negative acceleration decreases T ( ex: T = 2(-5+9.81)... T = 9.62
case #3 of tension problems: 2 tension forces at symmetrical angles
Tcosθ + Tcosθ - mg = may
2Tcosθ - mg = 0
T = mg/2cosθ
case #4 of tension problems: 2 tensions at non equal angles
(T1 is approx 45 degrees to the right of the vertical and T2 is exactly to the left (0 degrees)
step 1) develop an equation for each tension: T1 & T2
step 2) solve for y direction: T1cosθ - mg = 0
T1 = mg/cosθ
step 3) solv for x direction: T1sinθ - T2 = 0
T2 = T1sinθ
step 4) since we solved for T1 in step 2(T1=mg/cosθ), we can plug this into the equation from step 3 to result in T2 = (mg/cosθ)sinθ..... Sin/Cos = tan so the equation becomes T2 = mg(Tanθ)
what is this
action force
what is this
reaction force
what law does this demonstrate?
Newton's 3rd law
rules for 2 body problems
~ the second law of motion must be developed for each individual body and simultaneously solve the resulting equations
~ if the 2 objects are connected by an inextensible string then they have a common acceleration so the system approach can be used.
what is the system approach
∑F(external) = (∑mi) x a(system)
ijk notation
i = x direction
J = y direction
k = z direction
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