Lecture 3 Motion & Net force

Lecture 3Motion & Net force

PS 300Spring 2019

1/29/19

PS 300-Homework

Unit 1Chapter 1

Suggestion problem set:4-9,14, 22-29, 34, 40, 44, 48, 50, 58, 62, 68, 86, & 88.

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Quantifying Properties: Measurements

• Measurement— numerical value with unitsex- 6.003 grams

• We will mainly be using the metric system which includes:

The meter, m, for length measurements

The gram, g, for mass measurements

The liter, L, for volume measurements

The Density Concept

• The density of an object is a measure of its concentration of mass.

• Density is defined as the mass of an object divided by the volume of the object.

Density =volume

mass

𝝆 =𝒎

𝑽

ρ (rho) is the symbol for density

V is the symbol for volume

m is the symbol for mass

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What mass of mercury (density 13.6

g/cm3) will occupy a volume of 25.0 mL?

Example—Density

Given

25.0 mL

Know

13.6g/mL

Mass of Mercury

?

m

Vρ

Moving objectsNon-moving objects

Science

A way of thinking about and understanding your environment (objects).

Objects have properties unique to that given object (e.g., size, color, density, mass…)

Taking measurements makes the collection of data more precise

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Conceptual

Physical

Science6th Edition

Chapter 1:

PATTERNS OF

MOTION AND

EQUILIBRIUM

This lecture will help you understand:

• Aristotle on Motion• Galileo’s Concept of Inertia• Mass—A Measure of Inertia• Net Force• The Equilibrium Rule• Support Force• Dynamic Equilibrium• The Force of Friction• Speed and Velocity• Acceleration

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Forces - Historical Background

Aristotle• Heavier objects

fall faster• Objects moving

horizontally require continuously applied force

• Relied on thinking alone

False

Describing Motion

• What we want to know?

• At rest or moving– speeding up? How fast

– slowing down? How slow?

– turning? direction?

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Moving objects

When an object moves, it goes from point A to point B – that is the DISTANCE it traveled. (SI unit is the meter)

Distance is how much ground an object has covered during its motion.

AB

A

B

50 mdisplacement

100 m

distance

Distance vs Displacement

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Displacement vs. Distance

• Distance is the length of the path that an object travels

• Displacement is the change in position of an object

Speed and Velocity

• Speed is described as the distance covered per amount of travel time.

distance coveredtravel time

Speed =

Units are : m/s

sdt

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The World’s Fastest Land Animal:

• The cheetah• Speed: up to 70 miles/hour• Metric equivalent: 31m/s (113 km/hour)

The World’s Fastest Water Animal:

• The Sailfish• Speed: up to 68 miles/hour• Metric equivalent: 30 m/s (109 km/hour)

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The World’s FastestFlying Animal:

• The Peregrine Falcon• Speed: up to 200 miles/hour during a dive!• Metric equivalent: 89 m/s (322 km/hour)

The World’s FastestProduction Street-legal Car (2017):• HENNESSEY VENOM F5: 301 MPH

• equivalents: 134.6 m/s

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The NEWEST World’s FastestHuman Being (2009):

• Usain Bolt: Jamaica

• Speed: Ran the 100 meter dash in 9.58 seconds!

• -

Formula for Calculating SpeedSpeed = Distance time

s td

Speed

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Velocity

• Velocity:

Speedometer Compass

How fast it is moving and direction of motion

Ex: 30 mph, east

v td

Velocity

Speed v. Velocity

1. How are speed and velocity similar?They both measure how fast something is moving

2. How are speed and velocity different?Velocity includes the direction of motion and

speed does not (the car is moving 5mph East)

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Speed and Velocity

• Average speed– is total distance traveled divided by travel

time

– equation:

average speed =

• Instantaneous speed– is speed at any instant of time

total distance coveredtravel time

Describing Motion— Displacement & Velocity

Displacement (m) vs time (s)

Time (s)

Dis

tan

ce

(m

)

Time (s)

Time (s)

Dis

tan

ce

(m

)D

ista

nc

e (

m)

Velocity (m/s) vs time (s)

Time (s)

Ve

loc

ity (

m/s

)

Time (s)

Time (s)

Ve

loc

ity (

m/s

)V

elo

cit

y (

m/s

)

Acc (m/s2) vs time (s)

Time (s)

Ac

c.

(m/s

2)

Time (s)

Time (s)

Ac

c.

(m/s

2)

Ac

c.

(m/s

2)

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The average speed in driving 30 km in 1 hour is the same average speed as driving

A. 30 km in one-half hour.

B. 30 km in two hours.

C. 60 km in one-half hour.

D. 60 km in two hours.

Speed and Velocity

CHECK YOUR NEIGHBOR

Calculating Acceleration

Acceleration = Change in velocity

Total timeSo…Acceleration = (Final speed – Initial speed)

Time

a t

Δv= vf-vi

t

vva if −

=

a: acceleration

vf: final velocity

vi: initial velocity

t: time

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Units of Acceleration

The SI unit for acceleration is m/s2.

Acceleration =

change of velocitytime interval

Acceleration

Galileo first formulated the concept of acceleration in his experiments with inclined planes.

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Acceleration

• Acceleration:A change in velocity. Or acceleration measures how fast velocity changes

• How an object accelerates?

-Speeding up

-Slowing down

-Changing direction

Calculations◼ A roller coaster starts down a hill at 10 m/s.

Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration?

GIVEN:

vi = 10 m/s

t = 3 s

vf = 32 m/s

a = ?

WORK:a = (vf - vi) ÷ t

a = (32m/s - 10m/s) ÷ (3s)

a = 22 m/s ÷ 3 s

a = 7.3 m/s2

avf - vi

t

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Motion

A B C

E

35 mphD

0 mph

45 mph

No friction

A→ B

B→ C

C→ D

D→ E

s, v, Acc., F + Eq.,?

At A

Wall

Fcar on wall =

Acceleration and velocity are actually

A. much the same as each other.

B. rates, but for different quantities.

C. the same when direction is not a factor.

D. the same for free-fall situations.

Acceleration

CHECK YOUR NEIGHBOR

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Net Force and Equilibrium

Force = mass x AccelerationKg x m/s2

Newton

The Concepts of Force and Net Force

• A force is something that is capable of changing an object’s state of motion, that is, changing its velocity.

• Force is measured in Newtons (N).

• The Net Force (Fnet) is the sum of all the forces acting on an object.

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Net Force

3N

5N

8N

3N

-5N

- 8N

3N

5N8N

A cart is pushed to the right with a force of 15 N while being pulled to the left with a force of 20 N. The net force on the cart is

A. 5 N to the left.

B. 5 N to the right.

C. 25 N to the left.

D. 25 N to the right.

Net Force

CHECK YOUR NEIGHBOR

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The Equilibrium Rule

The equilibrium rule:

The vector sum of forces acting on a non-accelerating object or system of objects equals zero.

Mathematical notation: F = 0.

The equilibrium rule, F = 0, applies to

A. vector quantities.

B. scalar quantities.

C. Both of the above.

D. Neither of the above.

The Equilibrium Rule

CHECK YOUR NEIGHBOR

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The equilibrium rule, F = 0, applies to

A. vector quantities.

B. scalar quantities.

C. Both of the above.

D. Neither of the above.

Explanation:

Vector addition takes into account + and – quantities that can cancel to zero. Two forces (vectors) can add to zero, but there is no way that two masses (scalars) can add to zero.

The Equilibrium Rule

CHECK YOUR ANSWER

When you stand on two bathroom scales, with one foot on each scale and weight evenly distributed, each scale will read

A. your weight.

B. half your weight.

C. zero.

D. actually more than your weight.

Support Force

CHECK YOUR NEIGHBOR

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Free Fall

• Occurs when an object falls unimpeded.

• Gravity accelerates the object toward the earth.

Acceleration• Free fall

– When the only forceacting on a fallingobject is gravity, (with negligible air resistance),the object is in a state of free fall.

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AccelerationCHECK YOUR NEIGHBOR

If a falling object gains 10 m/s each second it falls, its acceleration is

A. 10 m/s.

B. 10 m/s per second.

C. Both of the above.

D. Neither of the above.

AccelerationCHECK YOUR NEIGHBOR

A free-falling object has a speed of 30 m/s at one instant. Exactly one second later its speed will be

A. the same.

B. 35 m/s.

C. more than 35 m/s.

D. 60 m/s.

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