Measuring Motion: Position, Velocity, and Acceleration in PHY 101, Study notes of Physics

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PHY 101 Lecture #

Motion

PHY 101 Lecture #3:

Motion

Prof. Peter R. Saulson [email protected]

http://physics.syr.edu/courses/PHY101/ Off. Hrs: Tues 10 –11:30, Physics 263-4, 3-

PHY 101 Lecture #

Motion

Outline

Motion

How to measure itPositionVelocityAcceleration

PHY 101 Lecture #

Motion

Describing an object

For simplest purposes, an object is characterized

byits total amount of matter, or

mass

, and by

the

positio

n of its center of mass.

Mass

stays constant for most objects; measure it with a balance. (Mass of racquetball = 0.044 kg.)

PHY 101 Lecture #

Motion

Describing an object’s position

Measure how far an object is from some

reference point (“the origin”), along a set ofreference directions (“coordinate axes”.) (If motion is really simple, one distance is all

that is needed. If more complicated, needmore than one coordinate.)

PHY 101 Lecture #

Motion

Motion measurement using

video capture

Video cameras record a snapshot each 1/30 sec.Play back one frame at a time.Measure position of object as it appears in each

frame. Make

• table of positions at each instant of time– graph of the entries in the table

PHY 101 Lecture #

Motion

Motion of dropped ball

frame

time (sec) height (m) 0

1

2

3

4

5

6

7

8

9

10

11

12

PHY 101 Lecture #

Motion

Displacement

Motion

means change of position. We describe

change of position during an interval of timeas the

displacement

∆

r , defined as

r f

is the position at the end of the interval, and r^0

is the position at the beginning of the interval of time.

r

r

r

f

PHY 101 Lecture #

Motion

Calculating the velocity of

a moving object

Average velocity

is the displacement of the object

in an interval of time, divided by the durationof the time interval. From video data, calculate it from the difference

in position in two successive frames,divided by 1/30 sec. Ex.: average velocity from frame 0 to frame 1:

. sec/ m (^3). 0

sec (^30) / 1

m (^02). 1 m (^01). 1

−

−

= v

PHY 101 Lecture #

Motion

Average velocity of dropped ball The velocityof thedropped ballsteadilydecreases.(Steadilygreaterspeed, but ina negativedirection.)

PHY 101 Lecture

Motion

Instantaneous velocity

An object’s velocity isn’t necessarily the same

over a whole measurement interval. Often,we care most about its

instantaneous velocity

,

(This is the average velocity calculated over the

tiniest imaginable interval of time.) Although most interesting, instantaneous

velocity can’t be measured directly. Weusually substitute average velocity over asmall interval of time, e.g. 1/30 of sec.

.

lim

0

t

t^

∆ ∆

=

→ ∆

r

v

PHY 101 Lecture #

Motion

Acceleration of dropped ball

The dropped ball’s velocity decreases steadily

( i.e.

it grows in size, but with negative sign.)

A steady change in velocity is a constant

acceleration, in this case at(9.8 m/sec)/sec, or 9.8 m/sec

This is

g

, the

gravitationalacceleration at theEarth’s surface.

PHY 101 Lecture #

Motion

Where does

F

m

a

come in?

An object in

free fall

feels only the force of

gravity (i.e., its weight.) So the total (or net)force on the ball is just

F

net

=

W

=

m

g

.

Newton’s 2

nd

Law says

Thus, a freely falling object hasor, in other words,

a

=

g

. The ball falls

downward with the “acceleration of gravity.”

a

F

m

net

a

g

m

m