Day 2, Physics 131

HW Problem 1-8

Velocity is related to acceleration and distance by the following expression: v2 = 2axp. Find the power p that makes this equation dimensionally consistent.

HW Problem 1-18

What is the area of a circle of radius (a) 1.437 m and (b) 3.8 m?

HW Problem 1-30

A Jiffy: The American physical chemist Gilbert Newton Lewis (1874 – 1946) proposed a unit of time called the “jiffy.” According to Lewis, one jiffy = the time it takes for light to travel one centimeter.

(a)If you perform a task in a jiffy, how long has it taken in seconds?

(b)How many jiffys are in one minute?

Use speed of light, c = 2.9979 x 108 m/s.

HW Problem 1-39

You’ve just won the $12 million cash lottery, and you go in to pick up the prize. What is the approximate weight of the prize if you requested payment in

(a)quarters?(b)dollar bills?

State your assumptions!

HW Problem 1-46

A Porsche sports can can accelerate at 14 m/s2. (a)Is this acceleration greater than, less than, or

equal to 14 ft/s2? Explain.(b)Determine the acceleration of a Porsche in ft/s2.(c)Determine the acceleration in km/hr2.

HW Problem 1-55

Using a Cricket as a ThermometerThe “most accurate” cricket is the snowy tree cricket. Its rate of chirping is

N = number of chirps in 13.0 seconds= T - 40.0

Your pet cricket chirps 112 times in one minute (60.0 s). What is the temperature in degrees Fahrenheit?

HW Problem 2-6

A child rides a pony on a circular track whose radius is 4.5 m.

(a)Find the distance traveled and the displacement when the child has gone halfway around the track.

(b)Does the distance traveled increase, decrease, or stay the same when the child completes one circuit of the track?

(c)Does the displacement increase, decrease..?(d)Find the distance and displacement after one

complete circuit of the track.

HW Problem 2-17

A finch rides on the back of tortoise, which walks at a pace of 0.060 m/s. After 1.2 minutes the finch tires of the tortoise’s slow pace and takes flight in the same direction for another 1.2 second at 12 m/s. What is average speed of the finch for the 2.4-minute interval?

HW Problem 2-38

Running with an initial velocity of +11 m/s, a horse has an average acceleration of -1.81 m/s2. How long does it take for the horse to decrease its velocity to 6.5 m/s?

HW Problem 2-47

Starting from rest, a boat increases its speed to 4.12 m/s with constant acceleration.

(a)What is the boat’s average speed?(b)If it takes the boat 4.77 s to reach this speed,

how far has it traveled?

HW Problem 2-56

A rocket blasts off and moves straight upward from the launch pad with constant acceleration. After 3.0 s the rocket is at a height of 77 m.

(a) What are the magnitude and direction of the rocket’s acceleration?

(b) What is its speed at this time (3.0 s)?

HW Problem 2-64

The infamous chicken is dashing toward home plate with a speed of 5.8 m/s when he decided to hit the dirt. The chicken slides for 1.1 s, just reaching the plate.

(a)What are the magnitude and direction of the chicken’s acceleration?

(b)How far did the chicken slide?

Got Tutoring !

• See advising.unca.edu/pt• > request additional tutoring• > fill out application for additional tutoring

• The math lab, 3rd floor, north-east end, is run by math folks who know a lot of physics and are happy to help. “Send them up” was the response to my question. BTW, they also have coffee in the middle of the day.

The Physics of Baseball

“Baseball is a game of absolutely flat planes, perfect right angles, precise distances, measured velocities, and beautiful parabolas. Euclid would have loved baseball. …. Baseball demonstrates repeatedly all the physical laws of motion. It could have served as Newton’s laboratory. The fact that it’s played by flawed and unpredictable human beings creates a classically dramatic tension between the physical and the emotional, the fixed and the random. A single game of baseball is a whole repertoire of one-act morality plays. The good guys win about half the time, which seems to me to reflect the ways of the world.” “Follow the Sharks,” by William G. Tapply

2014: LA Angels, 0.605, AZ Diamondbacks , 0.395

Motion II, a lab we have skipped: “Up and Down the Incline”

•There is always gravity, in the amount of 9.81 m/s2, in the laboratory. Even when the little car is stopped for a jiffy at the top of the slope, the force of gravity is still present. The acceleration of gravity points down. •Please define “up” as “positive,” “down” as “negative.”

Figure 2-19

• Position, velocity and acceleration of a lava bomb as functions of time.

• Figure illustrates effect of gravity (constant acceleration downward) on the position and velocity of object(s) launched straight upward.

Freely Falling Objects, Section 2-7

• A ball is thrown straight up at 20.0 m/s.• ? How long to reach peak height ?

• ? On the way back down how fast is it traveling when it passes the thrower’s hand ?

Two ways to solve for max height

• Given: baseball travels straight up• Given: 3 s to the top.

• ? Initial velocity ?• ? Max height ?

• Use 2.7, 2.11, 2.12

Tallest Building in the Worldin Dubai

• Given fountain whose water goes up to 90 feet, about 27.5 m

• ? What is the exit velocity of the water ?

Word to the Wise

Excellent review of Chapter 2 on page 45!

See review pages when studying for tests!

Coordinate Systems

• Cartesian – x, y, z• Polar – r, • Sailing/geographic – N, S, E, W, SW, etc.

Vector Arithmetic

• Vectors have Magnitude and Direction• Section 3.2 Illustrates adding components of

vectors to add and subtract.

Cartesian vs. Polar• A point is located in a polar coordinate system by

the coordinates r = 2.5 m and = 35o. • Find the x- and y-coordinates of this point,

assuming the two coordinate systems have the same origin.

Note: Right triangles in this course

Careful of significant figures – don’t report an answer that has more sigfigs than the given material.

Commuter airplane

• Starts at O• Fly to city A, 175 km away in a direction 30.0o

north of east.• Then fly 150 km 20.0o west of north to B.• Then fly 190 km due west, to C.? Location of C relative to starting point, O ?? Find both distance and direction ?? Find total displacement for the trip ?

? How far is C from A ?

• Given: A –> B = 200 m• Given B –> C = 300 m• Given

• ?How far is C from A ?• ? Relative to A, what direction is C ?

Unit Vectors

• Magnitude 1• Directed right along one of the three

Cartesian axes, x, y, or z

Relative Motion

A river flows due east at 1.5 m/s. A boat crosses the river from the south short to the north shore by maintaining a constant velocity of 10 m/s due north relative to the water.

(a)? What is the velocity of the boat relative to the shore ?

(b)? If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?

Chapter 4, Two-Dimensional Kinematics

• Horizontal and vertical motion are completely independent of each other

Parabolic Trajectory• Air resistance ignored• Acceleration due to gravity is constant,

downward, = 9.81 m/s2

• Earth’s rotation is ignored.

Horizontal and Vertical Motion are Independent of each other

Zero Launch Angle

• “Foolish Frank” Example• Frank runs horizontally off cliff• Cliff is 50 m high• Frank lands in the river 15 m from the bottom

of the cliff? How fast was Frank running when he left the

cliff ?

Rifle

• A high-powered rifle fires a bullet with a muzzle speed of 1.00 km/s. The rifle is pointed horizontally at a large bull’s eye target 200 m away.

• ? How far below the extended axis of the rifle barrel does thee bullet hit the target ?

Fast Ball

• One of the fastest recorded baseball pitches was clocked at 101.0 mi/hr, 45.14 m/s.

• x = 60.5 feet, 18.44 m? Thrown initially horizontally, how much does

the pitch drop as it travels to home plate ?

4-4 General Launch Angle

• x = ( vo cos ) t

• vx = vo cos

• vx2 = vo

2 cos2

• y = ( vo sin ) t – ½ gt2

• vy = vo sin – gt

• vy2 = vo

2 sin2 - 2gy

Equations 4-10

Lee Child, in a “Reacher” Novel

• Gossip was flowing. There had been a giant explosion. Air Force radar in Colorado Springs had detected metal fifteen thousand feet up. It had hung there for a long second before falling back to earth.

• Or perhaps a jiffy!