Download Lecture 8: Forces & The Laws of Motion

Lecture 20:
CONCEPT REVIEW
Questions of Yesterday
1) Two women of equal mass are standing on the same hard wood
floor. One is wearing high heels and the other is wearing tennis shoes.
Which statement is NOT true?
a) both women exert the same force on the floor
b) both women exert the same pressure on the floor
c) the normal force that the floor exerts is the same for both women
2) A boulder is thrown into a deep lake. As the rock sinks deeper and
deeper into the water what happens to the buoyant force?
a) it increases
b) it decreases
c) it stays the same
Overview
One Dimensional Motion
Vectors
Two Dimensional Motion
Forces & Newton’s Laws
Work & Energy
Momentum
Rotation
Torque
One Dimensional Motion
Displacement & Distance
Velocity & Speed
Acceleration
Motion Graphs (d vs. t, v vs. t, a vs. t)
Constant Acceleration Motion
v = v0 + at
Dx = v0t + 1/2at2
v2 = v02 + 2aDx
Free fall (1D motion under force of gravity)
a = g = -9.8 m/s2
Vectors
Vector Representation in 2 Dimensions
Head-to-Tail Vector Addition
Vector Components
Vector Algebra using Components
Two Dimensional Motion
Displacement & Distance
Velocity & Speed
Acceleration
Constant Acceleration Motion
vx = v0x + axt
Dx = v0xt + 1/2axt2
vx2 = v0x2 + 2axDx
vy = v0y + ayt
Dy = v0yt + 1/2ayt2
vy2 = v0y2 + 2ayDy
Projectile Motion (2D motion under gravity)
2
a
=
g
=
-9.8
m/s
ay = 0
y
Relative Velocity
Force & Newton’s Laws
Newton’s 1st Law & Inertia
Newton’s 2nd Law: F = ma
Newton’s 3rd Law: F12 = -F21
Free Body Diagrams
Gravitational Force
Normal Force
Tension
Friction
Translational Equilibrium
Work & Energy
Work
Kinetic Energy
Work-Energy Theorem
Nonconservative Forces
Work done by Friction
Gravitational Potential Energy
Mechanical Energy Conservation
Elastic Potential Energy
Momentum
Momentum & Force
Impulse & Change in Momentum
Conservation of Momentum
Elastic Collisions
Inelastic Collisions
Perfectly Inelastic Collisions
Energy Conservation in Collisions
2 Dimensional Glancing Collisions
Rotation
Angular Displacement & Linear Displacement
Angular Velocity & Tangential Velocity
Angular Acceleration & Tangential Acceleration
Constant Angular Acceleration Motion
= 0 + at
Dq = 0t + 1/2at2
2 = 02 + 2aDq
Centripetal Acceleration
Centripetal Force: Newton’s 2nd Law
Circular motion with varying tangential speed
Torque
Torque & Angular Acceleration
Right-Hand Rule
Equilibrium Conditions
Rotational Analog to Newton’s 2nd Law: t = Ia
Moment of Inertia
Rotational Kinetic Energy
Work-Energy Theorem
Conservation of Mechanical Energy
Angular Momentum & Torque
Conservation of Angular Momentum
Lecture 1: Questions of the Day
1) If an equation is not dimensionally correct, does that mean
that the equation can’t be true?
A) YES
B) NO
2) You walk 10 m in a direction 20o North of East, you want to
know how far North you have traveled…
What trig function would you use to figure this out?
A) Sine
B) Cosine
C) Tangent
Lecture 2: Questions of the Day
1a) Is it possible to have +/- velocity and ZERO acceleration?
a) YES
b) NO
1b) Is it possible to have ZERO velocity and +/- acceleration?
a) YES
b) NO
2) What is the average velocity <v> in this plot?
a) vf
v (m/s)
b) vf/2
c) between 0 and vf/2
vf
d) between vf/2 and vf
vf/2
0
t (s)
Lecture 3: 1D Free Fall Concepts
If I throw a ball straight up in the air…
a) What is the velocity of the ball when it reaches its highest
point?
b) What is the velocity 1 s before reaching the highest point?
c) What is the change in its velocity during this 1 s interval?
d) What is its velocity 1 s after reaching its highest point?
e) What is the change in its velocity during this 1 s interval?
f) What is the change in velocity during the 2 s interval?
g) What is the acceleration of the ball during c), e), and f)?
Lecture 3: 1D Free Fall Concepts
If I throw a ball straight up in the air:
By how much does the speed decrease with each second while
ascending?
By how much does the speed increase with each second while
descending?
How much time is required for rising compared to falling?
Does the distance between 1 s intervals increase, decrease, or
stay the same while ascending?
Does the distance between 1 s intervals increase, decrease, or
stay the same while descending?
Lecture 3: Questions of the Day
1) A skydiver jumps out of a hovering helicopter and a few
seconds later a second skydiver jumps out so they both fall
along the same vertical line relative to the helicopter.
1a) Does the difference in their velocities:
a) increase
b) decrease
c) stay the same
1b) What about the vertical distance between them?
2) I drop ball A and it hits the ground at t1. I throw ball B
horizontally (v0y = 0) and it hits the ground at t2. Which is
correct?
a) t1 < t2
b) t1 > t2
c) t1 = t2
Lecture 4: Questions of the Day
1) Can a vector A have a component greater than its magnitude
A?
a) YES
b) NO
2) What are the signs of the x- and y-components
of A + B in this figure?
a) (x,y) = (+,+)
b) (+,-)
c) (-,+)
d) (-,-)
Lecture 5: Projectile Motion
At what point in the object’s trajectory is the
speed a minimum?
What about velocity?
t= 1 s
t= 2 s
t= 3 s
t= 4 s
t= 5 s
Lecture 5: Projectile Motion
A projectile falls beneath the straight-line path it would follow if
there were no gravity. How many meters does it fall below
this line if it has been traveling for 1 s? For 2 s?
Does your answer depend on the angle at which the projectile
is launched? What about the speed?
t= 1 s
t= 2 s
t= 3 s
t= 4 s
t= 5 s
Lecture 5: Questions of the Day
1) Two projectiles are thrown with the same initial speed, one at
an angle q with respect to the ground and the other at an
angle 90o - q. Both projectiles strike the ground at the same
distance from the projection point. Are both projectiles in the
air for the same length of time?
a) YES
b) NO
2) A heavy crate is dropped from a high-flying airplane as it flies
directly over your shiny new car? Will your car get totaled?
a) YES
b) NO
Lecture 6: Questions of the Day
1) A ball is thrown vertically upwards in the air by a passenger on a
train moving with a constant velocity. To a stationary observer
outside the train, is the velocity of the ball at the top of its trajectory
a) greater than
b) Less than
c) Equal to
the velocity observed by the passenger?
2) The hang-time of a basketball player who jumps a vertical distance
of 2 ft is about 2/3 second. What will the hang-time be if the
player reaches the same height while jumping 4 ft horizontally?
a) less than 2/3 s
b) greater than 2/3 s
c) equal to 2/3 s
Lecture 7: Newton’s 2nd Law
If an object is accelerating does that mean that there has to be
a net force on it?
If an object is not accelerating does that mean that no forces
are acting on it?
I apply a force F1 to my physics book to push it across the desk
with a velocity of 10 m/s.
If instead I want to push the book at a velocity of 20 m/s is the
force I need to apply
greater than, less than, or equal to F1?
Lecture 7: Newton’s 3rd Law
If a Mack Truck and Honda Civic have a head-on collision,
upon which vehicle is the impact force greater?
Which vehicle experiences the greater acceleration?
Lecture 7: Questions of the Day
1) You must apply a force F1 to begin pushing a crate from
rest across the floor, you must apply a force F2 to keep
the crate moving at a constant velocity once its in
motion. Which statement is true?
a) F1 = F2
b) F1 > F2
c) F1 < F2
2) When are action and reaction pairs of forces NOT equal
and opposite?
a) when one of the objects is accelerating
b) when both objects are accelerating
c) never
Lecture 8
How much do you weigh in a moving elevator?
A 50-kg person stands on a scale in an
elevator
Draw a free body diagram for the person
What does the scale read when
the elevator is:
a) at rest?
b) Ascending with a speed of 2.0 m/s?
c) Descending with a speed of 2.0 m/s?
d) Ascending with an acceleration of 2.0 m/s2?
e) Ascending with an acceleration of 2.0 m/s2?
Lecture 8: Questions of the Day
You must apply a force F to push your physics book across your desk at a
constant velocity.
1a) The net force acting on the book is…
a) F
b) between 0 and F
c) greater than F
d) 0
1b) Are other forces acting on the book in the horizontal direction?
a) YES
b) NO
c) not enough information to know
2) A large crate is at rest in the bed of a truck. As the truck accelerates the
crate remains at rest relative to the truck. In what direction is the net force
on the crate?
a) the same direction as the truck’s acceleration
b) opposite the direction of the truck’s acceleration
c) the net force is zero
Lecture 9: Questions of the Day
1) A student pushes her physics book across a flat table.
Another student pushes his book up a 30o inclined plane.
Assuming the coefficient of kinetic friction is the same in both
cases, in which case is the force of friction acting on the book
greater?
a) the book on the flat table
b) the book on the inclined plane
c) the force of friction is the same in both cases
2) If you hold your physics book up against the chalkboard, in
what direction is the force of friction directed?
a) upwards
b) downwards
c) away from the chalkboard
d) into the chalkboard
Work done by Friction
A block slides down the inclined plane at a constant velocity.
What forces are acting on the block along the incline?
What is the work done by each of the forces?
What is the net work Wnet done on the block
over the distance d?
M
d
M
q
Wnc + Wc = KEf - KEi = DKE
Lecture 10: Questions of the Day
1) You slam on your brakes in a panic and skid a certain distance d
down a straight and level road before coming to a stop.
If you had been traveling twice as fast, what would the skidding
distance be?
a) 2d
b) d/2
c) 4d
d) d/4
2) As a pendulum swings back and forth, the forces acting on the
pendulum are the force of gravity and tension in the supporting
cord. Which of these forces does no work on the pendulum?
a) Gravity
b) Tension
c) neither one does work on the pendulum
d) they both do work on the pendulum
Lecture 11: Questions of the Day
1) A 50-kg student starting from rest slides down a frictionless
waterslide of height 10 m while a 100-kg student slides down
a similar slide that is only 5 m high.
Which student is going faster when they reach the bottom?
a) the 50-kg student
b) the 100-kg student
c) they are going the same speed
2) A women pulls a crate up a rough (with friction) inclined plane
at a constant speed. Which statement is NOT true?
a) The work done on the crate by the normal force of the
inclined plane on the crate is ZERO
b) The work done on the crate by gravity is ZERO
c) The work done by the net force on the crate is ZERO
d) The gravitational PE is increasing
Lecture 12: Questions of the Day
1) A mass with speed v hits a horizontal spring and compresses it a
distance d. If the the speed of the mass were doubled (2v) what
would the compression distance be?
a) 4d
b) 2d
c) d
d) d/2
2) A mass on a spring is oscillating back and forth from x = -d to x = d?
At what point in the oscillation is the speed of the mass the
greatest?
a) x = d
b) x = -d
c) x = 0
d) x = d and x = -d
Lecture 13: Questions of the Day
A 50-kg object is traveling with a speed of 100 m/s and a 100-kg
object is traveling at a speed of 50 m/s.
1a) Which object has more momentum?
1b) Which object has more kinetic energy?
a) 50-kg object
b) 100-kg object
c) they are equal
2) Would a head-on collision between two cars be more
damaging to the occupants if the cars stuck together or if the
cars rebounded upon impact?
a) if the cars stuck together
b) if the cars rebounded
c) both collisions would be equally damaging
d) it depends on the relative masses of the cars
Lecture 14: Questions of the Day
1) A piece of clay traveling north with speed v collides perfectly
inelastically with an identical piece of clay traveling east with
speed v. What direction does the resultant piece of clay travel?
a) north
b) east
c) 45o N of E
d) 45o S of W
2) If Ball 1, moving with an initial speed v, collides with Ball 2 which is
initially at rest, which scenario is not possible following the
collision?
a) Both balls are moving
b) Ball 1 is at rest and Ball 2 is moving
c) Ball 2 is at rest and Ball 1 is moving
d) Both balls are at rest
Rotational Motion

Which position has a greater angular displacement
in a given time interval?
What about angular speed? Angular acceleration?
Rotational Motion

Which position has a greater angular displacement
in a given time interval?
What about angular speed? Angular acceleration?
Lecture 15: Questions of the Day
1) You are going through a vertical loop on roller coaster at a constant
speed. At what point is the force exerted by the tracks on you (and
the cart you are in) the greatest?
a) at the highest point
b) at the lowest point
c) halfway between the highest and lowest point
d) the force is equal over the whole loop
2) You are on a merry-go-round moving at constant speed. If you move
to the outer edge of the merry-go-round, what happens to the net
centripetal force keeping you on the merry-go-round?
a) it increases
b) it decreases
c) it stays the same
d) there is no net centripetal force acting on you
Lecture 16: Questions of the Day
You are riding on a Ferris wheel moving at constant speed.
1a) At what point is the net force acting on you the greatest?
a) the top
b) the bottom
c) halfway between top and bottom
d) the force is the same over the whole motion
1b) Is the net force doing work on you?
a) YES
b) NO
2) If the mass of the moon were doubled, what would happen to
its centripetal acceleration?
a) it would increase
b) it would decrease
c) it would stay the same
Lecture 17: Questions of the Day
1) If an object is rotating at a constant angular speed which
statement is true?
a) the system is in equilibrium
b) the net force on the object is ZERO
c) the net torque on the object is ZERO
d) all of the above
2) Student 1 (mass = m) sits on the left end of massless seesaw
of length L and Student 2 (mass = 2m) sits at the right end.
Where must the pivot be placed so the system is in
equilibrium?
a) L/2
b) L/3 from the right (from Student 2)
c) L/3 from the left (from Student 1)
d) the system cant be in equilibrium
Lecture 18: Moment of Inertia
I = mr2
r
r
F
m
F
m
Which object has a greater Moment of Inertia?
If the same force F is applied to each object as shown…
which object will have a greater angular acceleration?
Rotational Kinetic Energy
Sphere radius = R
Is = (2/5)mR2
Cube length
= 2R
m
m
h
h
q
q
What forms of energy does each object have….
at the top of the ramp (before being released)?
halfway down the ramp?
at the bottom of the ramp?
What is the speed of each object when it reaches the bottom of
the frictionless ramp (in terms of m,g, h, R and q)?
Which object reaches the bottom first?
Angular Momentum
R
M
1
R
2 = ?
M
You (mass m) are standing at the center of a merry-go-round (I =
(1/2)MR2) which is rotating with angular speed 1, as you walk to
the outer edge of the merry-go-round…
What happens the angular momentum of the system?
What happens the angular speed of the merry-go-round?
What happens to the rotational kinetic energy of the system?
Lecture 18: Questions of the Day
1) A solid sphere and a hoop of equal radius and mass are both rolled
up an incline with the same initial velocity. Which object will travel
farthest up the inclined plane?
a) the sphere
b) the hoop
c) they’ll both travel the same distance up the plane
d) it depends on the angle of the incline
2) If an acrobat rotates once each second while sailing through the air,
and then contracts to reduce her moment of inertia to 1/3 of what is
was, how many rotations per second will result?
a) once each second
b) 3 times each second
c) 1/3 times each second
d) 9 times each second
Questions of the Day
1) Ball 1 is thrown vertically in the air with speed v. Ball 2 is thrown
from the same position with the same speed v but at an angle of
45o. Which ball is in the air longer?
A) Ball 1
B) Ball 2
C) they are in the air for the same amount of time
D) it depends on the magnitude of v
2) A pendulum swings back and forth in a circular arc. How does the
tension in the pendulum string at the highest point compare to the
tension at the bottom of the swing?
A) the tension is greater at the highest point
B) the tension is less at the highest point, but not zero
C) the tension is the same at both points
D) the tension is zero at the highest point