Section 1
Preview this deck
In which shape of motion does an object with constant velocity in one direction and constant acceleration in another direction go?
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
6 years ago
Date created
Mar 14, 2020
Cards (204)
Section 1
(50 cards)
In which shape of motion does an object with constant velocity in one direction and constant acceleration in another direction go?
a parabola
W=Fx W=area of the graphs W=∆k (change in kinetic energy) therefore... Graph A has the least change in kinetic energy b/c the area is the smallest.
The graphs shown are all drawn to the same scale, representing the net force F as a function of displacement x for an object moving along a straight line. Which graph represents the least change in kinetic energy of the object from x=0 to x=x1? Why?
What equation do you use to find work?
W=Fx W is work, F is force, x is displacement Because force and displacement are both vectors and you are taking the dot product of the two, they must be parallel. The value you get for work will be a scalar.
Negative sign you have to watch for!
F=-dU/dx
How do you find the area of a graph given the equation for the function?
add one to exponent then divide
If F₁ is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F₂ is the magnitude of the force exerted by the satellite on the Earth, then what is true?
F₁ is equal to F₂
If a box is sliding up a frictionless ramp, its conservation of energy equation would be?
1/2 mv^2=mgh m=mass h=height v=velocity g= acceleration due to gravity
Two spheres are launched a the same time and from the same height. One is launched with a horizontal speed, v₀, from the height, while the other sphere is dropped. What can be determined about their time of flight?
The spheres will land at the same time, because while one sphere is launched with a v₀ in the x-direction, the spheres both experience the same vertical motion. Vertical motion is what determines the time of flight and since it is equal for the two spheres, their time in the air is equal.
What is linear momentum and what is it's equation?
Linear momentum is a mass in motion. p=mv(x) p=mv(y) p: momentum (Ns) m: mass (kg) v: velocity in both (x) and (y) direction because linear momentum is a vector!
What is the equation to find the velocity of the center of mass?
Vcm=∑(v*m/Mtot) Vcm-velocity center of mass equals the some of the systems' particles: velocity*mass
What is the kinetic energy equation?
k=(1/2)mv² k=kinetic energy (J) m=mass (kg) v= velocity (m/s)
A yo-yo at the top of the swing. Write Newton's 2nd Law
mg+T=ma
When do you feel heavy on an elevator? When do you feel light?
You feel heavy when you accelerate upward, because the normal force, the force you feel, is greater than weight. You feel light when you accelerate downward.
When does center of mass stay stationary?
When there are no external forces.
Given a Force vs. Displacement graph, how can work done by a spring's force be calculated?
The work can be calculated by finding the area under the curve. Why? Because Work is the integral of a Force vs. Displacement graph (power rule backwards).
What is the equation for centripetal acceleration?
a(subscript)c= v²÷r a(subscript)c: centripetal acceleration v: speed r: radius *Remember, this is only for things changing directions-not for speeding up or slowing down
Mass M₁ is moving with speed v toward stationary mass M₂. The speed of the center of mass of the system is...
(M₁÷(M₁+M₂))v
What is a vector?
a quantity with magnitude and direction
What happens when the velocity vector of an object is in the same direction as the acceleration vector of an object?The opposite direction? Perpendicular?
When the velocity and acceleration vectors are in the same direction, the object is speeding up. When these vectors are in the opposite directions, the object is slowing down. When they are perpendicular to each other, the object is turning around.
Centripetal force is ____ to the velocity
Perpendicular
When an object is at equilibrium what MUST be true about the object? Why?
The object must have an acceleration of 0 and no net force acting on it. This is commonly mistaken with the object must be at rest or moving with a constant velocity. The object could be moving with a constant velocity or remain at rest.
"Derive a differential equation" means...
Write your Newton 2nd Law equations and substitute a=dv/dt
What is the angle of maximum range for a surface with no vertical displacement?
45°
To stretch a certain nonlinear spring by an amount x requires a force F of F=5x²-17x+3, where F is in newtons and x is in meters. What is the equation for the work done?
Work is the backwards power rule (integral) of a force equation. Work is the change in potential energy. W=(5x³/3)-(17x²/2)+3x
What is the equation when the mechanical energy of a system is conserved?
U+K=U+K
what does negative velocity tell you?
that the object is moving to the left
If a book is being pushed against a wall, the normal force would be?
Perpendicular to the wall
When do you draw a best fit line? Does a best fit line have to go through the origin?
-In general, we fit lines to data to determine slope -rearrange an equation to get the meaning of slope (change of y divided by x) -Does not need to go through the origin
What is the slope of a position versus time graph?
velocity
Approach for Boat problems
center of mass does not move! set reference point that doesn't move, then write center of mass equation for before and after mass redistribution.
Define center of mass.
The center of mass is the average position of a system's mass
How can ∆velocity be calculated given an acceleration v. time graph?
To calculate ∆velocity on an acceleration v. time graph, determine the area under the graph on the needed interval.
If an object's displacement vs. time graph is linear, what is its acceleration?
0 m/s²
What angle is max range off a cliff?
less than 45 degrees
What does turning around look like on a velocity vs. time graph?
Crossing the x-axis.
What does the area of a Force/Time Graph represent?
Impulse
When astronauts are in space, they are in...
free fall
Are the following terms vectors or scalars? distance speed work
scalars
Does the center of mass have to remain in your body?
No. For example, when high jumpers arch their body in a U shape to clear the bar, their center of mass actually goes under the bar. This allows them to jump really high.
The position of a particle moving in a xy plane is given by r=(6t³+3t)i+(5-2t²)j with position in meters and time in seconds. Write the expression for the acceleration as a function of time.
First, take the derivative of the position equation to find the velocity expression as a function of time. v=(18t²+3)i+(-4t)j Next, take the derivative of the velocity equation to find the acceleration of the particle as a function of time. a=(36t)i+(-4)j
Write Newton's 2nd Law equations for the following situation: Bob pulling a block on a frictionless horizontal surface at an angle.
N+Fsinθ-mg=0 Fcosθ=ma
How do you find the average acceleration of a acceleration vs. time graph?
Area/time
The object changes direction twice because the velocity changes signs (crosses the x-axis) twice.
How many times does the object change direction?
What is power?
Power is the rate of energy transfer, measured in watts. P=∆W/t P=Fv W is work (Joules) t is time (seconds) F is force (Newtons) v is velocity (m/s)
How do you convert degrees to radians?
(degrees given)/(180/π)
The acceleration of a particle traveling along the x-axis is expressed by the equation a=12t. If the particle starts moving at position x=3 with a velocity of 4 m/s, what is its position at t=10 seconds?
x=2043m Do power rule backwards...don't forget about initial position and velocity! v=6t^2 +4 x=2t^3 + 4t + 3
In which shape of motion does an object with constant velocity in one direction and constant velocity in another direction go?
a straight line
What quantity is the area of a velocity vs time graph?
displacement
What is drag force and how is it found?
Drag force is a force opposite to relative motion through a medium.( fluid, air...) the equation for Drag Force is usually given on ap note that, at terminal velocity D=mg because acceleration =0
What is the difference between conservative and nonconservative forces?
Conservative forces are forces that change energy from potential energy to kinetic energy (gravity). Nonconservative forces, such as friction, are forces that change energy to heat. If there is no nonconservative forces present, then U+K at one point equals U+K at every other point.
Section 2
(50 cards)
First kinematics equation (constant acceleration) no displacment
This is also average acceleration (slope of the second line of a velocity vs time graph)
Second kinematics equation (constant acceleration) no final velocity
most often used for projectile motion
Work for rope falling off table
if lifting rope divide by 2 λ stands for linear density
If a block of mass M with velocity V has an elastic collision with a stationary block of mass M, what is the second block's final velocity?
V
instantaneous acceleration
Slope of the Tangent line power rule forwards (multiply by exponent then subtract one) 2nd derivative of position as a function of time
velocity of center of mass
Instantaneous velocity
slope of the Tangent line Power rule forward (multiply by exponent then subtract one)
Calculus: Definition of Center of Mass
λ stands for linear density
tangential acceleration
When is momentum conserved during an interaction?
When the net external force equals zero
Defining a Potential Energy
negative work
Definition of Average Power (algebra)
Algebra: Definition of Center of Mass
What can be found by determining the instantaneous slope of a Velocity vs. Time graph?
the instantaneous Acceleration
total acceleration
no angular acceleration
Calculus: Definition of Work
Definition of Work (algebra)
dot product!
conversion for linear and angular velocity
Algebra: Definition of Moment of Inertia
Newton's 3 Laws
Force of static Friction
static friction is a variable force! Only as strong as it needs to be
Elastic Potential Energy for Hooke's Law spring
Block A is moving at a constant velocity V₀. The block then collides with block B, of the same mass, and stick together in an elastic collision. What is the new velocity of the two blocks?
V₀/2
Dot Product
multiply parallel vectors then add for SCALAR answer=56 Joules
Force of kinetic friction
depends on materials and normal force acting on object
Impulse-Momentum
Cross Product
use matrix to multiple perpendicular vectors to get a vector answer 3Nmi-6Nmj+3Nmk
conversion between translational displacement and angular displacement
Finding force given potential energy as a function of position
Negative Sign!
Finding Position given velocity versus time equation
Area of velocity vs time plus initial position power rule backwards (add one and then divide by exponent) + initial condition
Definition of Instantaneous Power
Fourth Kinematics Equation (constant acceleration) no acceleration
conservation of energy with friction
Weight
depends on location and planet
average velocity
average velocity is the slope of the secant line
Hooke's Law
Newton's Second Law, traditional
linear/tangential velocity for circular motion
T is period= time for one complete circle
Newton's Second Law, calculus
Is a high jumper's center of mass at at the peak of their jump stable or unstable?
unstable
radial/ centripetal acceleration
Conservation of Mechanical energy
potential loss is kinetic gained
Third kinematics equation (constant acceleration no time)
A rock explodes, sending two pieces, one of mass M and one of mass 3M, in two opposite directions. How does the center of mass change after the explosion?
The center of mass doesn't change
Work-Energy Theorem
angular acceleration definition (calculus)
Gravitational Potential Energy
energy from power
Calculus: Definition of Moment of Inertia
lambda stands for linear density
Final velocity from acceleration vs time equation
area of acceleration vs time plus initial condition power rule backwards (add one then divide by exponent) + initial condition
Section 3
(50 cards)
What are the 3 possibilities for the motion of an object that accelerates?
Speeding up Slowing down Change direction
What is the conservation of energy equation for a block of mass M going downward by a height of H onto a lower floor right into spring of spring constant K
mgh+1/2mv^2=fx+1/2kx^2
What force acts on an object in the air? WHat is the direction of this force?
Gravity Down
definition of torque (calculus)
Which force is the strongest? a.Max Static Friction b. Static Friction c. Kinetic Friction
a Max static friction
Acceleration (calculus speak)
Instead of writing "a" write dv/dt because its the change of velocity over the change in time
The car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. the initial acceleration of the stone, as it leaves the surface of the road, is: a. Vertically upward b. Horizontally forward c. Horizontally backward d. Zero e. Upward and forward at approximately 45⁰ to the horizontal
a. Vertically upward The acceleration of a rotating object always points toward the center of rotation.
What does perfectly inelastic mean?
The two objects stick together after collision.
Why do we feel like we are being pushed onto the side of a car when we turn? Doesn't that mean that we're accelerating outward?
no you're feeling the normal force, and the car's centripetal force is causing it.
If you had to construct a lab based on the conservation of energy, specifically the transformation of ths energy from potential to kinetic, what tool(s) would be necessary? a. Meterstick b. Different masses c. Electronic balance d. Stopwatch e. Track
Meterstick and Stopwatch
If a block is being tugged by a string on top of another block which rests on a friction-less plane, the force acting on the lower block is equal to the ________ of the upper block.
Force of friction.
Rotational Kinetic energy
What does the negative derivative of a potential energy vs. position graph represent?
Force
A constant slope on a velocity vs time graph means what in terms of acceleration?
A horizontal line acceleration graph
Given the position of an object as a function of time, how would you find the acceleration of that object?
Power rule (forwards) twice. Doing the power rule gives you the slope of the function. The slope of a position vs. time graph is velocity. The slope of a velocity vs. time graph is acceleration.
In a collision based on momentum, if the masses stick together does the final velocity compared to their initial velocities increase, decrease, or stay the same?
decrease
Velocity when rolling without slipping
Rotational Inertia of rod: Calculus
λ stands for linear density
An object is moving along a horizontal surface with no friction and hits another object that is stationary. They stick together and keep moving. Which is true? A. Momentum only is conserved B. Momentum and energy are conserved C. Energy alone is conserved D. Neither can be conserved
A. Momentum only is conserved
If a man jogs from his house to Starbucks, gets a coffee, and takes an alternative route home, what his displacement?
dx=0
What is the force of contact?
The point force at the point of contact between two objects. By newtons third law the forces act equaly and oppositely.
The relationship between acceleration and velocity is given by the equation a(t)=4t^3+3t^2+t. What is the equation for the relationship between displacement and time? Negate any unknown constants.
x(t)=(1/5)(t^5)+(1/4)(t^4)+(1/6)(t^3)
What is the difference between an elastic collision and an inelastic collision?
In an inelastic collision only momentum is conserved. In a elastic collision both momentum and energy are conserved.
How can we find rotational inertia?
rotational inertia is mR^2. I=inertia I=∫(r^2)dm
How do you find tangential velocity using arc length?
v=2πr/T
For a nonlinear spring, the relationship between force and displacement is given by the equation F=3k(x^5). what is the amount of work down be stretching the spring distance d? A) 3k(d^5) B) (1/3)k(d^5) C) (3/5)k(d^5) D) .5k(d^6) E)3k(d^6)
correct answer: d
What is the vertical velocity of a projectile at its highest point?
v= 0, zilch, nada
How does the center of mass of an object change if only internal forces are acting on the object?
The center of mass does not change if only internal forces act on the object. Only external forces can change the center of mass.
What does an instantaneous slope on a position vs. time graph mean?
Instantaneous velocity at that time. Derive the position equation WITH RESPECT TO TIME and plug in time to find the velocity at that point!
To stretch a certain nonlinear spring by an amount x requires a force F given by F=33x^2+20x-6x^2+1, where F is in Newtons and x is in meters. What is the change in potential energy ?
U=-11x^3-10x-2x^3-1x
If you have a block of mass y over a spring that is compressed a distance x vertically, find the spring constant.
Kx = yg K=(yg)/(x) Set up your newton's second law equations and solve for K.
Can we assume that every collision where the objects bounce is an elastic colison? Why or why not?
No. Just because objects bounce doesn't mean energy is conserved. For example, in Newton's cradle, the balls bounce but eventually stop colliding, which means energy was lost in the system or the balls would collide forever.
angular momentum for system
At one moment, someone on the ground sees an object falling with a velocity v. A plane flying sees it falling at v1 at an angle to the ground. How fast is the plane going?
You make a velocity triangle with v1 as your hypotenuse v as your vertical leg. Use pythagorean to find your unknown velocity, which is your plane. You get sqrt(v1^2-v^2) for the answer
Acceleration when rolling without slipping
Constant acceleration equations for rotation
ω= ωo+αt θ= ωot+1/2αt2 ω2=ωo2+2α θ θ=1/2(ω+ ωo)t
How do you find the minimum speed to make it around a loop-de-loop?
mg=mv²/r g=v²/r v=√gr
net torque for system
What is the acceleration of a 100lb object when it reaches terminal velocity?
acceleration = 0
Free body equation for a large squirrel climbing a robe that is strung over a vertical indigo colored aluminum pole and has a treasure chest attached to the other end:
(Mg-mg=ma)
The slope of a work vs. time graph is:
Power. Because Work over Time is equal to power.
Definition of Torque, vector style
Definition of Angular momentum for point particle
The force for a spring is represented by the equation F=Ax^3+Bx. Derive an expression for potential energy as a function of x.
U=Ax^4/4+Bx^2/2
True or False? An object with velocity always has force.
False.
How do you calculate the spring constant of a hanging Hooke's Law Spring?
F = kx mg = kx k = (mg)/x
Parallel-Axis Theorem
kinetic energy for rolling object
What is the acceleration of an object in parabolic motion at the top of its arc?
X: 0 m/s^2 Y: -9.8 m/s^2 Therefore the net force is down
What are three possible motions for an object that has a net force?
Speed up, slow down, change direction
Section 4
(50 cards)
Completely Inelastic Collision
A collision where the two objects stick together after colliding.
What is the slope of a Force vs. Displacement graph? a. Velocity b. Work c. Spring Constant d. Kinetic Energy
c spring constant
What are the two types of friction?
Static (when the object is stuck) and kinetic (when the object is moving).
The integral of a velocity versus time equation is what?
The change in displacement of a position versus time function.
Two people shoot water guns at each other on skateboards on frictionless surfaces. By the end of the fight their distance will have... a) increased b) decreased c) stayed the same
a) increased
A 5kg box is on a frictionless incline plane. When the angle of the incline decreases will the normal force of the box increase or decrease?
Increases!
What are the three special cases for elastic collisions?
Equal masses: v1(final)=0 and v2(final)=v1(initial) Massive target: v1(final)=-v1(initial) and v2(final)=0 Massive projectile: v1(final)=v1(initial) and v2(final)=2v1(initial)
what is the slope of a Force displacement graph of a hook's law spring?
the spring constant K
Arlo pushes two blocks in contact with each other, one with a mass of m1 and another with a mass of m2, on a frictionless surface with a force of F. Write an equation for the acceleration of both blocks.
F=(m1+m2)a a=F/(m1+m2)
Which kind of equilibrium exists when a body is at rest on a hill? In a ditch? On the ground?
On a hill=unstable equilibrium. In a ditch= stable equilibrium. On the ground= neutral equilibrium.
What does the derivative of a velocity equation tell you?
Acceleration equation. Taking the derivative gives you the slope of the equation.
What will reach terminal velocity first, an elephant or a mouse?
The mouse. Terminal velocity is reached when an object's drag force equals its weight. The mouse weights less so it will take less time for its drag force to equal its weight
What does a freebody diagram look like for a book pushed against a wall (with the book on the left and the wall on the right)?
Pushing force going right (towards the wall), normal force going left (away from wall), weight going down, static friction going up.
What is terminal velocity?
The velocity of an object when drag force equals the downward force of gravity
What does the instantaneous slope of a momentum vs. time graph mean?
Force! Take the derivative (power rule) of your momentum equation to find the force.
What is impulse and what are a few formulas you can use to find it?
Impulse is the change in momentum. Impulse = Force x time Impulse = mass(final velocity) - mass(initial velocity) Impulse = area of a force/time graph (the integral)
What is terminal velocity?
The velocity at which an object with air resistance stops accelerating.
What is the tension when sitting on a bosun's chair?
The tension on each rope is equal and their sum has to equal the combined weight of you and the chair. So 2T=(your mass+chair mass)g, then T=mg/2
What determines the force of friction?
The material (µ) and the normal force
Area Under U vs x Means
Nothing
How does work relate to potential energy?
Work is the negative change in potential energy. W=-U
What does graph of projectile motion look like?
Parabola (example graph), only vertical force acting on it is g.
Are elastic collisions common in the real world? If not what is the closest thing we have to them? If they are common what is an example of one?
Elastic collisions are very rare. The closest thing we have to them in the real world is when two billiard balls strike each other.
Which of the following is not an energy equation? a) Fx b) -kx c) 1/2mv^2 d) mgh
Answer b is not an energy equation but Hooke's Spring Law equation. To get energy from this force equation, one must take the anti-derivative which will be -1/2kx^2
What is the area of a acceleration V mass graph
Force
What does positive work mean?
Object gains energy.
Why is a hooke's law equation always negative?
Because springs are always fighting the force you put on it
A billiard ball going 3m/s hits an identical billiard ball that is at rest. What are the final velocities of the two billiard balls?
Vfinal of 1st ball: 0m/s Vfinal of 2nd ball: 3m/s (V1f=0 ; V2f=V1i)
What are the types of vectors?
1. Displacement 2. Velocity 3. Acceleration 4. Force 5. Torque 6. Normal Force 7. Frictional Force 8. Momentum
What simple equation could you use to find the time elapsed for an object travelling at a constant speed over a given displacement?
x = vt x - displacement (m) v - velocity (m/s) t - time (s)
Equation for work done by a Hooke's Law spring
1/2kx^2 k is the spring constant x is the distance from the equilibrium point of the spring (compression)
Maria accidentally let go of her balloon at a birthday party. Write the equation for Newton's second law of the balloon rising with air resistance acting on it.
mg+D=ma mg= weight D= the force of air resistance m= the mass of the balloon a= the acceleration of the ballon
What is the difference when using backwards power rule when force is related to x, and when force is related to time.
When force is related to x, the result of the backwards power rule is work. When it's related to time, the result is impulse.
On a potential energy (J) v. displacement (m) graph, the values for a particle at Point A are (5, 3). At Point B, the values are (7, 8). What does this tell you?
After moving 5 meters, the particle gained 2 Joules of kinetic energy. Its elevation was raised.
Which two of the following are true if an object is in equilibrium? A. The object is at rest B. Zero acceleration C. Net force is zero D. The object is moving with a constant velocity
B and C
What is the center of mass of an object?
The average position of the mass.
Minimum speed to make around a loop-the-loop
mg=m(v^2/r) m cancels v=sqrt(gR) r=radius, m=mass, g=gravity(9.8), v=velocity
What would a graph of displacement look like if an object had a constant nonzero acceleration?
The graph of displacement would look like a parabola
What equation can be used for Elastic Collisions?
V1i+V1f=V2i+V2f
If the slope of a position versus time graph is linear, what would the graphs of the velocity versus time and acceleration versus time look like?
velocity versus time: horizontal line at some y value(slope of 0), there is a constant velocity acceleration: horizontal line on the x-axis, there is no acceleration
What does going from a positive to negative slope mean on a position vs time graph?
Changed direction (from going right to going left)
What is the normal force of a block on a inclined plane?
N=mgcosθ (not mg!)
What is the slope of a Friction vs Normal Force Graph?
The coefficient of friction Friction: (Coeff. of friction) * Normal force Friction/Normal = Coeff. of Friction
What are the three motions of an object with a net force?
An object with a net force can be speeding up, slowing down, or turning around.
When do you have to use energy conservation?
For springs when finding maximum compression, swinging objects, and roller coasters.
To find average velocity of an object:
Change in displacement (NOT Velocity) divided by the change in time
More time in a collision means what for the force?
The force will be less if the time of impact is longer in order to keep the impulse the same. Impulse is the change in momentum. J = Force X Time or mv - mv(initial)
What force do astronauts not have acting on them in space that they usually would have on earth?
A Normal force
Why to always wear a seatbelt
Newton's 1st law state an object in motion tends to stay in motion unless acted on by an outside force. Therefore if you don't wear a seat belt and get in a crash, your body will continue moving unless you are buckled up.
If a force is applied to one block which happens to be touching a second block, what is the equal and opposite force of each block on the other?
Force contact
Section 5
(4 cards)