Units_Conversions_xva.ppt

UNITS

A UNIT is nothing more than a standard by which a measured value can be

described.

1.British Engineering Units (feet, pound, second)

2.Standard International (SI) system (meter, gram, second)*

A useful method of converting one unit to an equivalent unit is called the

factor-label method.

Ex- how many seconds are in a year?

UNIT CONVERSION

A useful method of converting one unit to an equivalent unit is called the

factor-label method.

Ex- how many seconds are in a year?

UNIT CONVERSION

A useful method of converting one unit to an equivalent unit is called the

factor-label method.

Ex- how many seconds are in a year?

For simple, one step conversions, using the proportion method is also

acceptable.

UNIT CONVERSION

A useful method of converting one unit to an equivalent unit is called the

factor-label method.

Ex- how many seconds are in a year?

For simple, one step conversions, using the proportion method is also

acceptable.

Ex—Convert 5 m to cm

UNIT CONVERSION

1 min 31,536,000 _sec/yr

x cm 5 m

100 cm 1 m

1. Cross multiply, then solve for x (x cm)(1m) = (5m)(100cm)

All measurements have some degree of uncertainty.

Rules for Determining if a Digit is Significant

1.All nonzero digits are always significant

2.All final zeros used after the decimal point are always significant

3.Zeros between two other significant digits are always significant

4.Zeros used solely for spacing the decimal point are not significant

Ex – State the number of significant digits in each number

1. 56 sec

2. 101.3 m

3. 0.032 g

4. 345, 000, 203 cm

5. 0.1240 km

Ex – State the number of significant digits in each number

1. 56 sec 2

2. 101.3 m 4

3. 0.032 g 2

4. 345,000,203 cm 9

5. 0.1240 km 4

When measurements are either too

small or too large to read easily, we use scientific notation.

Rules for Proper Numbers in Scientific Notation

M x 10n 1 < M < 10; n is an

integer

1.Move decimal point until only one digit appears to left of decimal point

2.Count number of places the decimal

point was moved and use this number as the exponent, n

Examples:

Perform the following conversions 1. 0.00029 m

1. 31,678,000 m Examples:

Perform the following calculations 1. 5.7 x 104 _{m + 6.30 x 10}4 _{m =}

2. 7.4 x 106 m – 1.55 x 107 m =

3. 5.3 x 103 _{m * 9.3 x 10}4 _{m =}

4. 5 x 10-5 m =

6.440 x 10-2 _s

Examples:

Perform the following conversions 1. 0.00029 m 2.9 x 10-4 _m

1. 31,678,000 m 3.1678 x 107 _m

Examples:

Perform the following calculations

1. 5.7 x 104 _{m + 6.30 x 10}4 _{m = 1.2 x 10}5 _m

2. 7.4 x 106 m – 1.55 x 107 m = -8.1 x 106 m

3. 5.3 x 103 _{m * 9.3 x 10}4 _{m = 4.9 x 10}8 _m

4. 5 x 10-5 m = 7.76 x 10-4 m/s

6.440 x 10-2 _s

SCIENTIFIC NOTATION

Sometimes, in order to solve a problem, it is necessary to manipulate a given

equation.

Ex – Given v = d/t, solve for d

v = d *multiply through with t

t

vt = dt , t

d = vt

Ex – Solve for a

v_f = v_i +at

Ex – Solve for a

v_f = v_i +at

Move v_i over to other side of ‘=‘

at = v_f - v_i

divide by t on both sides of ‘=‘

a = v_f – v_i t

Every Graph should include:

1. Title 2. Scale

3. Labeled Axes 4. Labeled Units

5. Correctly Recorded Data

To find the slope of a line:

Slope = m = rise = y = (y2 – y1) run x (x2 – x1)

Ex – Find the slope of the line between t = 4 and t = 5

Ex – Find the slope of the line between t = 4 and t = 5

m = y = (y₂ – y₁) = (200 m– 150 m) = 50 m/s

x (x₂ – x₁) (5 s – 4 s)

Interpolation: creating new data points, or reading data, between defined data points.

Extrapolation: constructing new data

points outside of the defined set of data points

HEY! Everything moves!

HOW

LINEAR MOTION

THINGS

MOVE

Position

Velocity

x, d

LINEAR MOTION: POSITION

Meters

x

i

x

f

LINEAR MOTION: POSITION

x

i

x

f

x

i

x

f

d

i

d

f

d

i

d

f

x_i

x_f



x

LINEAR MOTION: POSITION



x

is

distance

LINEAR MOTION: VELOCITY

v

Meters/

second

LINEAR MOTION: VELOCITY

Speed

and

v

i

v

f

LINEAR MOTION: VELOCITY

Speed in a

certain

Direction

v

i

v

f

LINEAR MOTION: VELOCITY

V

avg

=



x

t

V

avg

=



x

t

V

avg

=



x

t

LINEAR MOTION: VELOCITY

Velocity’s Sign

y

x

positive

LINEAR MOTION: VELOCITY

Velocity’s Sign

y

x

LINEAR MOTION: ACCELERATION

a

Meters/

second

2

42

Speeding Up

&

Slowing Down

43

LINEAR MOTION:

ACCELERATION

a

avg

=



v

t

a

avg

=



v

t

a

avg

=



v

1

44

LINEAR MOTION: ACCELERATION

Acceleration’s Sign

1

2

2

positive

45

LINEAR MOTION: FREE FALL

•

Falling under the influence of

gravity alone

•

Pretend air resistance does not

46

g = 10 m/s

2*

*or when accuracy is needed, use g = 9.81 m/s2

LINEAR MOTION: FREE FALL

Gravity is the force of attraction

that pulls objects to each other

47

LINEAR MOTION: FREE FALL

Instantaneous

Velocity

48

LINEAR MOTION: FREE FALL

1

2

3

1. Ball is dropped from rest 2. Acceleration of gravity is

constant and downward, Velocity is increasing

49

LINEAR MOTION: FREE FALL

1 3

4

5 2

1. Ball is thrown straight up with an initial velocity

2. Acceleration of gravity is acting on ball; Velocity decreases

3. Direction of ball changes, velocity is zero;

Acceleration of gravity is still acting on ball

4. Velocity increases in opposite direction

5. Velocity increases;

50

LINEAR MOTION: FREE FALL

Whenever an object’s initial speed is zero and the acceleration is

constant, the equations for the

velocity and distance traveled are:

v = gt

51

LINEAR MOTION: FREE FALL

If the object has an initial velocity, vi,

the equations for velocity and distance become:

v = v

i

+ gt

52

V_avg = ____________ m/s

d_tot = ____________ m

53

10 20

30

40

V_avg = ____________ m/s

d_tot = ____________ m

5 80

physics-experiment-ball.htm

VECTORS