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Physics 114A - Mechanics Review for Exam1 (Walker: Chapters 1-4) January 23, 2014

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### Physics 114A - MechanicsReview for Exam1(Walker: Chapters 1-4)January 23, 2014

John G. Cramer

Professor Emeritus, Department of Physics

B451 PAB

Announcements

- Homework Assignment #2 is due at 11:59 PM on Thursday, January 23 (Tonight!).
- Three clickers that have been used in clicker sessions have unknown owners. They have clicker numbers: 613371, 682117, and 684611. If one of these is your clicker, send me email to register it. I have sent new email to 7 students who do not have registered clickers.
- My office hours are 12:30-1:20 PM on Tuesdays (i.e., the hour before this class) and Thursdays at 2:30-3:20 PM in the “114” area of the Physics Study Center on the Mezzanine floor of PAB A (this building). I’ll be there today after class.

Physics 114A - Review 01

About Exam 1

- On Friday, January 24 (tomorrow) we will have Exam 1, which covers Walker, Chapters 1-4 and my lectures 1-9.
- Exam 1 will have assigned seating. Seating assignments have been posted on Catalyst and posted on the doors of this room. Get your seat assignment before coming to Exam 1.
- Exam 1 is closed-book, but you may bring with you one page of notes on an 8½x11” sheet of paper (both sides). Also bring a Scantron sheet,a #2 pencil, and a scientific calculator with good batteries. Prepare your Scantron in advance.
- The exam copies will be on the tables in the back as you enter this room. Take one.
- Exam 1 will have a multiple-choice section (15 questions, 75 pts) based on lecture example problems, homework, and “two-dot” end-of-chapter problems in Walker. Circle your MC answers.
- Exam 1 will also have a free-response section (4 questions, 25 pts) based on “Conceptual Questions” from Walker requiring thoughtful written answers.

Physics 114A - Review 01

Clicker Question:War at Sea

1

2

A battleship simultaneously fires two shells at two enemy submarines. The shells are launched with the same initial velocity. If the shells follow the trajectories shown, which submarine gets hit first ?

(A) Submarine 1

(B) Submarine 2

(C) They are both hit at the same time

(D) It depends on the initial velocity

Physics 114A - Review 01

Units of Chapter1

Physics and the Laws of Nature

Units of Length, Mass, and Time

Dimensional Analysis

Significant Figures

Converting Units

Order-of-Magnitude Calculations

Scalars and Vectors

Problem Solving in Physics

Physics 114A - Review 01

Summary of Chapter 1

- Physics is based on a small number of laws and principles
- Units of length are meters; of mass, kilograms; and of time, seconds
- All terms in an equation must have the same dimensions
- The result of a calculation should have only as many significant figures as the least accurate measurement used in it

Physics 114A - Review 01

Dimensional Analysis (1)

Any valid physical equation must be dimensionally consistent – each side must have the same dimensions.

Basic Units:

Mass = M => kilogram = kg

Length = L => meter = m

Time = T => second = s

From the Table:

Distance = velocity × time

Velocity = acceleration × time

Energy = mass × (velocity)2

Physics 114A - Review 01

Dimensional Analysis (2)

Example:

The periodP(T)of a swinging pendulum depends only on the length of the pendulumd(L)and the acceleration of gravityg(L/T2).

Which of the following formulas forPcouldbe correct ?

P =2 (dg)2

(a)

(b)

(c)

Physics 114A - Review 01

Dimensional Analysis (3)

Remember that Pis in units of time (T), d is length (L) and g is acceleration (L/T2).

The both sides must have the same units

Try equation (a).

Try equation (c).

Try equation (b).

(a)

(b)

(c)

Physics 114A - Review 01

Units of Chapter 2

Position, Distance, and Displacement

Average Speed and Velocity

Instantaneous Velocity

Acceleration

Motion with Constant Acceleration

Applications of the Equations of Motion

Freely Falling Objects

Physics 114A - Review 01

Summary of Chapter 2 (1)

- Distance: total length of travel
- Displacement: change in position
- Average speed: distance / time
- Average velocity: displacement / time
- Instantaneous velocity: average velocity measured over an infinitesimally small time

Physics 114A - Review 01

Summary of Chapter 2 (2)

- Average acceleration: change in velocity divided by change in time
- Instantaneous acceleration: average acceleration measured over an infinitesimally small time
- Deceleration: velocity and acceleration have opposite signs
- Constant acceleration: equations of motion relate position, velocity, acceleration, and time
- Freely falling objects: constant accelerationg = 9.81 m/s2 downward

Physics 114A - Review 01

Velocity & Slope

The position vs. time graph of a particle moving at constant velocity has a constant slope.

4.5 m

The position vs. time graph of a particle moving with a changing velocity has a changing slope.

3.0 s

slope = velocity = 4.5 m/3.0 s = 1.5 m/s

Physics 114A - Review 01

Motion with Constant Acceleration

Average velocity:

(2-9)

Position as a function of time:

(2-10)

(2-11)

Velocity as a function of position:

(2-12)

Physics 114A - Review 01

Example: An Accelerating Train

A train moving in a straight line with an initial velocity of 0.50 m/s accelerates at 2.0 m/s2 for 2.0 s, coasts with zero acceleration for 3.0 s, and then accelerates at -1.5 m/s2 for 1.0 s.

(a) What is the final velocity vf of the train?

(b) What is the average acceleration aavof the train?

Physics 114A - Review 01

Position

Velocity

Acceleration

Freely Falling Objects

Trajectory of a projectile:

Physics 114A - Review 01

Units of Chapter 3

- Scalars Versus Vectors
- The Components of a Vector
- Adding and Subtracting Vectors
- Unit Vectors
- Position, Displacement, Velocity, and Acceleration Vectors
- Relative Motion

Physics 114A - Review 01

Summary of Chapter 3 (1)

- Scalar: number, with appropriate units
- Vector: quantity with magnitude and direction
- Vector components:Ax = A cos θ, By = B sin θ
- Magnitude: A = (Ax2 + Ay2)1/2
- Direction:θ = arctan(Ay / Ax)
- Graphical vector addition: Place tail of second at head of first; sum points from tail of first to head of last
- Component method:add components of individual vectors, then find magnitude and direction

Physics 114A - Review 01

Summary of Chapter 3 (2)

- Unit vectors are dimensionless and of unit length
- Position vector points from origin to location
- Displacement vector points from original position to final position
- Velocity vector points in direction of motion
- Acceleration vector points in direction of change of motion
- Relative motion: v13 = v12 + v23

Physics 114A - Review 01

Properties of Vectors

Physics 114A - Review 01

Example: Height of a Cliff

In Jules Vern’s Mysterious Island,Capt. Cyrus Harding wants to find theheight of a cliff. He stands with hisback to the base of the cliff andmarches straight away from it for 500 ft.At this point, he lies on the ground andmeasures the angle from horizontal tothe top of the cliff.

(a) If the angle is 34.0°, how high is the cliff?

(b) What is the straight line distance d from Capt. Harding to the top of the cliff?

Physics 114A - Review 01

Example: Car Acceleratingon a Curve

N (y)

E(x)

A car is traveling northwest at 9.00 m/s. Eight seconds later it has rounded a corner and is now headed north at 15.0 m/s/

(a) What is the magnitude and direction of the acceleration during those 8.0 s?

Physics 114A - Review 01

Example: Rounding a Curve

A car is traveling east at 60 km/h. It rounds a curve, and 5.0 s later it is traveling north at 60 km/h.(a) Find the average acceleration of the car.

Physics 114A - Review 01

Example: Crossing a River

You are riding in a boat with a speed relative to the water of vbw = 6.1 m/s. The boat points at an angle of q = 25° upstream on a river flowing at vwg = 1.4 m/s.

(a) What is your speed vbgand angle qbg relative to the ground?

Physics 114A - Review 01

Units of Chapter 4

- Motion in Two Dimensions
- Projectile Motion: Basic Equations
- Zero Launch Angle
- General Launch Angle
- Projectile Motion: Key Characteristics

Physics 114A - Review 01

Summary of Chapter 4

- Components of motion in the x- and y-directions can be treated independently
- In projectile motion, the acceleration is –g
- If the launch angle is zero, the initial velocity has only an x-component
- The path followed by a projectile is a parabola
- The range is the horizontal distance the projectile travels

Physics 114A - Review 01

Constant Acceleration

Physics 114A - Review 01

Constant Acceleration withax = 0 and ay = -g

Physics 114A - Review 01

Finding Position from Velocity

Physics 114A - Review 01

Zero Launch Angle

In the zero launch angle case, the initial velocity in the y-direction is zero. Here are the equations of motion, with x0 = 0 and y0 = h:

Physics 114A - Review 01

General Launch Angle

In general, v0x = v0 cos θand v0y = v0 sin θ

This gives the equations of motion:

Physics 114A - Review 01

g

R is maximum when qo=45o, so that sin 2qo = 1.

Horizontal Range of a ProjectilePhysics 114A - Review 01

t1Example: A Rough Shot

Chipping from the rough, a golfer sends the ball over a 3.0 m high tree that is 14.0 m away. The ball lands on the green at the same level from which it was struck after traveling a horizontal distance of 17.8 m.

(a) If the ball left the clubat 54.0° above the horizontaland landed 2.24 s later, what was its initial speed v0?

(b) How high was the ball when it passed over the tree?

Physics 114A - Review 01

gExample: A Home Run

A baseball is hit so that it leaves the bat making a 30° angle with the ground. It crosses a low fence at the boundary of the ballpark 100 m from home plate at the same height that it was struck. (Neglect air resistance.)

What was its velocity as it left the bat?

Physics 114A - Review 01

Example: Jumping a Crevasse

A mountain climber encounters a crevasse in an ice field. The opposite side of the crevasse is 2.75 m lower, and the horizontal gap is 4.10 m. To cross the crevasse, the climber gets a running start and jumps horizontally.

(a) What is the minimum speed v0 needed for the climber to cross the crevasse?

(b) Suppose the climber jumps at 6.0 m/s, where does he land?

(c) What is his speed on landing?

Physics 114A - Review 01

gExample: A Cap in the Air

A delighted physics graduate throws her cap into the air with an initial velocity of 24.5 m/s at a 36.9° angle with the horizontal. The cap is later caught by another student. [Neglect air resistance ; Sin(36.9°) = 3/5; Cos(36.9°) = 4/5]. (a) Find the total time the cap is in the air.(b) Find the total horizontal distance traveled.

Physics 114A - Review 01

Example: What A Shot!

The archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish’s mouth. Suppose an archerfish squirts water with an initial speed of 2.30 m/s at an angle of 19.5° above the horizontal. When the water reaches a beetle ata height h above the water’ssurface, it is moving horizontally.

- (a) How much time does the beetle have to react?
- What is the height h of the beetle?
- What is the horizontal distance d between the fish and the beetle?

Physics 114A - Review 01

Before Monday, read Walker Chapter 5.1-4.### End of Review 1

- Homework Assignment #2 should be submitted using the WebAssign system by11:59 PM on Thursday, January 23 (Tonight!).
- There are still a few unregistered clickers. Register your clicker by sending me your name, netID, 3-letter screen ID, and 6-digit clicker number by email,

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