Lecture 20: CONCEPT REVIEW

Questions of Yesterday1) 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 floorb) both women exert the same pressure on the floorc) 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 decreasesc) it stays the same

OverviewOne Dimensional Motion

Vectors

Two Dimensional Motion

Forces & Newton’s Laws

Work & Energy

Momentum

Rotation

Torque

One Dimensional MotionDisplacement & Distance

Velocity & Speed

Acceleration

Motion Graphs (d vs. t, v vs. t, a vs. t)

Constant Acceleration Motion

v = v0 + atx = v0t + 1/2at2

v2 = v02 + 2ax

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 MotionDisplacement & Distance

Velocity & Speed

Acceleration

Constant Acceleration Motion

vx = v0x + axtx = v0xt + 1/2axt2

vx2 = v0x

2 + 2axx

Projectile Motion (2D motion under gravity)ay = g = -9.8 m/s2

vy = v0y + ayty = v0yt + 1/2ayt2

vy2 = v0y

2 + 2ayy

ay = 0

Relative Velocity

Force & Newton’s LawsNewton’s 1st Law & Inertia

Newton’s 2nd Law: F = ma

Newton’s 3rd Law: F12 = -F21

Free Body Diagrams

Translational Equilibrium

Gravitational Force

Normal Force

Tension

Friction

Work & EnergyWork

Work-Energy Theorem

Kinetic Energy

Nonconservative Forces

Work done by Friction

Gravitational Potential Energy

Mechanical Energy Conservation

Elastic Potential Energy

MomentumMomentum & Force

Conservation of Momentum

Impulse & Change in Momentum

Elastic Collisions

Inelastic Collisions

Perfectly Inelastic Collisions

Energy Conservation in Collisions

2 Dimensional Glancing Collisions

RotationAngular Displacement & Linear Displacement

Angular Velocity & Tangential Velocity

Angular Acceleration & Tangential Acceleration

Constant Angular Acceleration Motion

Centripetal Acceleration

Centripetal Force: Newton’s 2nd Law

= 0 + t

= 0t + 1/2t2

2 = 02 + 2

Circular motion with varying tangential speed

TorqueTorque & Angular Acceleration

Right-Hand Rule

Equilibrium Conditions

Rotational Analog to Newton’s 2nd Law: = I Moment of Inertia

Rotational Kinetic Energy

Work-Energy Theorem

Angular Momentum & Torque

Conservation of Mechanical Energy

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) YESB) 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) CosineC) Tangent

Lecture 2: Questions of the Day1a) Is it possible to have +/- velocity and ZERO acceleration?a) YESb) NO1b) Is it possible to have ZERO velocity and +/- acceleration?a) YESb) NO

2) What is the average velocity <v> in this plot?a) vf

b) vf/2c) between 0 and vf/2d) between vf/2 and vf

t (s)

v (m/s)

vf

vf/2

0

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

Lecture 3: 1D Free Fall ConceptsIf 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 Day1) 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) increaseb) decreasec) 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 Day1) Can a vector A have a component greater than its

magnitude A?a) YESb) NO

2) What are the signs of the x- and y-components of A + B in this figure?

a) (x,y) = (+,+)b) (+,-)c) (-,+)d) (-,-)

A

B

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

Lecture 5: Projectile MotionA 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 Day1) Two projectiles are thrown with the same initial

speed, one at an angle with respect to the ground and the other at an angle 90o - . 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) YESb) 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) YESb) NO

Lecture 6: Questions of the Day1) 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 trajectorya) greater than

b) Less thanc) Equal tothe 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 sb) greater than 2/3 sc) equal to 2/3 s

Lecture 7: Newton’s 2nd Law

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?

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?

Lecture 7: Newton’s 3rd Law

Which vehicle experiences the greater acceleration?

If a Mack Truck and Honda Civic have a head-on collision, upon which vehicle is the impact force

greater?

Lecture 7: Questions of the Day1) 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 acceleratingb) when both objects are acceleratingc) never

Lecture 8How 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 DayYou 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 Fd) 0

1b) Are other forces acting on the book in the horizontal direction?a) YESb) NOc) 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 accelerationb) opposite the direction of the truck’s accelerationc) the net force is zero

Lecture 9: Questions of the Day1) 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 tableb) the book on the inclined planec) 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) downwardsc) away from the chalkboardd) into the chalkboard

Work done by Friction

What is the work done by each of the forces?

M

A block slides down the inclined plane at a constant velocity.What forces are acting on the block along the incline?

Md

Wnc + Wc = KEf - KEi = KE

What is the net work Wnet done on the block over the distance d?

Lecture 10: Questions of the Day1) 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/2c) 4dd) 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) Gravityb) Tensionc) neither one does work on the pendulumd) they both do work on the pendulum

Lecture 11: Questions of the Day1) 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 studentb) the 100-kg studentc) 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 ZEROb) The work done on the crate by gravity is ZERO c) The work done by the net force on the crate is ZEROd) The gravitational PE is increasing

Lecture 12: Questions of the Day1) 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) 4db) 2dc) 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 = -dc) x = 0d) x = d and x = -d

Lecture 13: Questions of the DayA 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 objectb) 100-kg objectc) 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 togetherb) if the cars reboundedc) both collisions would be equally damagingd) it depends on the relative masses of the cars

Lecture 14: Questions of the Day1) 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) northb) eastc) 45o N of Ed) 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 movingc) Ball 2 is at rest and Ball 1 is movingd) 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 Day1) 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 pointb) at the lowest pointc) halfway between the highest and lowest pointd) 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 decreasesc) it stays the samed) there is no net centripetal force acting on you

Lecture 16: Questions of the DayYou 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 bottomc) halfway between top and bottomd) the force is the same over the whole motion

1b) Is the net force doing work on you?a) YESb) NO

2) If the mass of the moon were doubled, what would happen to its centripetal acceleration? a) it would increaseb) it would decreasec) it would stay the same

Lecture 17: Questions of the Day1) If an object is rotating at a constant angular speed

which statement is true?a) the system is in equilibriumb) the net force on the object is ZEROc) the net torque on the object is ZEROd) 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

Which object has a greater Moment of Inertia?

I = mr2

rm m

r

If the same force F is applied to each object as shown…which object will have a greater angular acceleration?

F F

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?

Rotational Kinetic Energy

h h

What is the speed of each object when it reaches the bottom of the frictionless ramp (in terms of m,g, h, R and

)?

Which object reaches the bottom first?

m mSphere radius = R

Is = (2/5)mR2

Cube length = 2R

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?

Angular Momentum

R

M

R

M

1 2 = ?

Lecture 18: Questions of the Day1) 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 sphereb) the hoopc) they’ll both travel the same distance up the planed) 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 secondc) 1/3 times each secondd) 9 times each second

Questions of the Day1) 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 1B) Ball 2C) they are in the air for the same amount of timeD) 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 pointB) the tension is less at the highest point, but not zeroC) the tension is the same at both pointsD) the tension is zero at the highest point