FORCE and Motion

A force is the effect that may produce a change in the motion state, the size, or the shape of a body.

• A force is just a push or pull. Examples:– an object’s weight– tension in a rope– friction– attraction between an electron and proton– Force is a vector!

• Bodies don’t have to be in contact to exert forces on each other these are called Field Forces, e.g., gravity.

Objects at Rest

An object remains at rest because the forces acting on it are balanced; not because there are NO forces acting upon it

The downward force (mg) of gravity is balanced by an upward force of the table (-mg).

Acceleration

Acceleration is the rate of change in velocity: A change in speed (magnitude) A change in direction A change in both magnitude (speed) and direction

Newton’s First Law (Inertia law)

• The velocity of an object remains unchanged unless acted upon by a net force.

or….• An object will experience

acceleration if acted upon by a net force.

Inertia Example 1

An astronaut in outer space will continue drifting in the same direction at the same speed indefinitely, until acted upon by an outside force.

Inertia Example 2IF YOU’RE DRIVING AT 100 KMPH AND HAVE AN ACCIDENT, YOUR CAR MAY COME TO A STOP IN AN INSTANT, WHILE YOUR BODY IS STILL MOVING AT 100 KMPH. WITHOUT A SEATBELT, YOUR INERTIA COULD CARRY YOU THROUGH THE WINDSHIELD.

Newton’s Second Law

F = ma

The Second Law of Motion"Force equals mass times acceleration

(Fnet = ma): The net force on an object is equal to the mass of the object multiplied by its acceleration."

Unitsm = mass = kilogram (kg)a = acceleration = m/s2

Fnet = force = ma = kg∙m s2

{Fnet} is sometimes written as {SF} or

Resultant Force R.F.

= Newton (N)

R.F. = m*a• The acceleration of an object is directly

proportion to the net force acting on it (slide 15).• For a given mass, if Fnet doubles, triples, etc., so

does a.• The acceleration of an object is inversly

proportion to its mass(a = Fnet /m).• For a given R.F. , if m doubles, a is cut in half.• R.F. and a are vectors; m is a scalar.• R.F. and a always point in the same direction.

** Graph of Fnet vs. aIn the lab various known forces are applied—one at a time, to the same mass—and the corresponding accelerations are measured.

The data are plotted. Since Fnet and a are

directly proportional, the relationship is linear.

F

a

** Mass = Slope

F

a

Since slope (rise / run) = F / a, the slope is equal to the mass.

so [m = F / a]

F

a

Newton’s Third Law

"Every action has an equal and opposite

reaction"

The 3RD Law Restated

Forces always occur in pairs. If object A exerts a force F on object B, then object B exerts an equal and opposite force –F on object A.

Action – Reaction examples:• If you hit a tennis ball with a racquet, the

force on the ball due to the racquet is the same as the force on the racquet due to the ball, except in the opposite direction.

• If you fire a rifle, the bullet pushes the rifle backwards just as hard as the rifle pushes the bullet forwards.

• If you drop an apple, the Earth pulls on the apple just as hard as the apple pulls on the Earth.

Examples: 1. Lost in Space

Suppose an International Space Station astronaut is on a spacewalk when her tether snaps. Drifting away from the safety of the station, what might she do to make it back?

2. Swimming

Due to the 3rd Law, when you swim you push the water (blue), and it pushes you back just as hard (red) in the forward direction. The water around your body also produces a drag force-resistance- (green) on you, pushing you in the backward direction. If the green and red cancel out, you don’t accelerate (2nd Law) and maintain a constant velocity.

Note: The blue vector is a force on the water, not the on swimmer! Only the green and red vectors act on the swimmer.

3. The Slam Dunk

1. The player exerted a downward force against the earth (court)

2. The earth exerted a reciprocal, upward force upon the player

3. The force exerted by the earth elevated the player to the rim!

4. Demolition Derby

When two cars of different size collide, the forces on each are the SAME (but in opposite directions). However, the same force on a smaller car means a bigger acceleration!

What is Net (Resultant) Force?When more than one force acts on a body, the net force (resultant force) is the vector combination of all the forces.

i.e. the resultant force is the single force that has the same effect as all of the forces acting on the object.

F1

F2

F3

Fnet

Resultant Force (cont.)• When forces act in the same line, we can just add or subtract their

magnitudes to find the net force.

Resultant Force (cont.)• When two perpendicular forces (F1 & F2) act on an object, the magnitude of the net force is: Fnet = ( F1

2 ) + ( F22 ) , and it’s

direction is between the two forces.

Examples of net forces:

Net Force & the 2nd Law

Example 1. Find the acceleration of the object in the figure.

Fnet = 32 + 10 – 15 = 27 N to the right

a = Fnet /m = 27/2 = 13.5 m/s2, to the right.

2 kg

15 N 32 N

10 N

50 Kg

Example 2. Find the acceleration of the object in the figure.

80 N

60 N

Fnet = ( F1

2 ) + ( F22 ) = ( 802 ) + ( 602 ) = 100 N

a = Fnet /m = 100/50 = 2 m/s2, direction shown in fig.

Fnet

The forces on this

hanging crate are balanced.

Balanced forces:

When two forces acting on an object are

equal in size but act in opposite

directions, we say that they

are balanced forces. If the forces on an object are balanced

(or if there are no forces acting on it)

this is what happens: an object that is not moving stays still an object that is moving continues to

move at the same speed and in the same

directionNotice that an object can be moving

even if there are no forces acting on it.

Examples:Here are some examples of balanced

forces.

1. Hanging objectsThe forces on this hanging crate are equal

in size but act in opposite directions. The

weight pulls down and the tension in the

rope pulls up.

2. Floating in water

Objects float in water when their weight is balanced by the upward force from water called “upthrust”. The object will sink if its weight is greater than the upthrust force.

A boat floats because its weight is balanced by the upthrust from the water

Unbalanced forces:

When two forces acting on an object are not equal in size, we say that they are unbalanced forces.

If the forces on an object are unbalanced (net force ≠0) this is what happens:an object that is not moving (at rest) starts to movean object that is already moving changes velocity.

Unbalanced forces make the truck speed up (net force > 0)

Free fall

•An object is in free fall if the only force acting on it is gravity.•{air resistance is negligible }

Acceleration Due to Gravity

The acceleration due to gravity, g, is constant for objects near the Earth’s surface :

g = 9.8 m/s2

Example: A Ball Drop

** Acceleration Sign Chart

AccelerationSign

Moving upwards

+

Moving downwards

-Accelerating +(Speeding up)

(++)=+

(-+)=-

Decelerating -(Slowing down)

(+-)=- (--)=+

Acceleration due to Gravity:Near the surface of the Earth, all objects accelerate at the same rate (ignoring air resistance) : { a = -g = -9.8 m/s2 }

This acceleration vector is the same if the object is thrown upwards or downwards! because downwards (-), the object is Accelerating (+) (a) is (-). Also, upwards(+), the object is Decelerating(-) (a) is (-).

- 9.8 m/s2

Galileo

Galileo dropped two cannon balls of different weights from the top of Leaning Tower of Pisa. The two cannon balls reached the ground at the same time. He proved that when objects of different weights are dropped at the same height and time, they take the same amount of time to fall to the ground (ignoring air resistance).

** Speed against time graph for free falling object

In the absence of air resistance any body falling freely under gravity falls with a constant acceleration. A graph of speed against time is shown below

The acceleration is equal to the gradient of the graph = 9.8 m/s2 (the magnitude of the free fall acceleration)

Mass and Weighto Mass measures the amount of matter in an object,

it’s a scalar quantity. o Weight is the force of gravity on a body, it’s a vector

quantity, it points toward the center of Earth.o Weight = mass acceleration due to

gravity(this follows directly from F = m a).

• E.g. A body has a mass 120Kg,

what is its weight on earth?

• W = mg = 120 X 9.8 ≈ 120 x 10 = 1200 Newton

** Mass and Weight (cont.)

On the moon, your mass would be the same, but your weight would be less, this is because the gravity of the moon is less than the gravity of Earth. gmoon ≈ 1/6 gearth ≈ 1.6 m/s2

W(on moon) ≈ 1/6 W(on earth)

Hippo & Ping Pong Ball

In vacuum, all bodies fall at the same rate.

When there’s no air resistance, size and shape don’t matter!

If a hippo and a ping pong ball were dropped from a helicopter in a vacuum (assuming the copter could fly without air), they’d land at the same time.

** Air Resistance ( drag force) It’s the friction force on an object

moving through air (or a fluid)

Although we often ignore air resistance ( R), it is usually significant in real life.

R depends on:• Speed (directly proportional to v2).• cross-sectional area• air density• other factors like shape

mg

m

R

Terminal Velocity

R

mg

This means the frog’s velocity can’t change any more. He has reached his terminal velocity. Small objects, like raindrops and insects, reach terminal velocity more quickly than large objects.

Suppose a frog jumps out of a skyscraper window. At first v = 0, so R = 0 too, and a = -g. As the frog speeds up, R increases, and his acceleration decreases. If he falls long enough his speed will be big enough to make R = mg. When this happens the net force is zero, so the acceleration must be zero too.

The speed against time graph for a falling parachutist

• In reality gravity is not the only force acting on any body falling through air, there is also air resistance.

(1) The parachutist jumps from the aircraft with his parachute closed.

(2) Speed increases, air resistance increases, the acceleration decreases.

(3)&(4) Steady (terminal) speed, air resistance = weight, net force = 0, acceleration = 0.

(5) The parachutist opens his parachute. The air resistance increases suddenly, the

parachutist starts to decelerate rapidly, speed decreases.

(6) The parachutist still slowing down .

(7) & (8) The parachutist reaches terminal speed, which is less than the speed in (3).

1000 N

1000 N

Forces & Motion

1. Find net force (by combining vectors).2. Calculate acceleration (using: Fnet = m×a).

3. Use kinematics equations:a=(v2-v1)/t orv2= v1+ a t d = v1t + a t2

V22 = v1

2 + 2 a dd = average V * t

Average V = ½ (v2+v1)

To solve motion problems involving forces:

2

1

(t = time of motion)(v2 = final velocity)

(v1= initial velocity)

(d = distance travelled by object)

(a = acceleration)

Samples Problem

a. R.F. (Fnet )

b. a

c. (v) after 5 s

d. (d) after 5 s

Samira 400 N

Fadi 1200 N

Samia 850 N

Treasure 300 kg

= 50 N left

=1/6=0.167 m/s2 left

=5/6=0.835 m/s left

1. Tow girls are fighting with a boy over a treasure box, initially at rest. Find:

=25/12=2.08 m left

Sample Problems (cont.)2. You’re riding a unicorn at 16 m/s and come to a uniform

stop at a red light 20 m away. What’s your acceleration?3. A brick is dropped from 80 m up. Find its impact velocity

and air time.4. An arrow is shot straight up from a pit 12 m below ground

at 18 m/s.a. Find its max height above ground.b. At what times is it at ground level?

5. A catcher catches a 36 Kmph fast ball. His glove compresses 5 cm. How long does it take to come to a complete stop? Answers: Q2. a = -6.4 m/s2. Q3. v = 40 m/s, t = 4 s. Q4. (a) d = 16.2 m, (b) t = 3.6 s. Q5. t = 0.01 s.

Remember the converging rules:(m/s) x (3.6) Km/h(Km/h) ÷ (3.6) (m/s)(cm) ÷ 100 (m)(m) X 100 (cm)

** Multi-step Problems1. How fast should you throw a kumquat

straight down from 40 m up so that its impact speed would be the same as a mango’s dropped from 60 m?

2. A dune buggy accelerates uniformly at 1.5 m/s2 from rest to 22 m/s. Then the brakes are applied and it stops 2.5 s later. Find the total distance traveled.

19.8 m/s

188.83 m

Answer:

Answer:

Fun Freefall Problems!!!!1) A ‘coin’ is dropped from the top of a rollercoaster.

The height of the ride is 110m. Neglecting air resistance, Find:

a. The speed of the coin when it hits the ground.

b. The time it takes for the coin to fall to the ground.

c. Would it be different for a heavier coin?Answers: (a) 44.7 m/s. (b) 4.47 s.

(c) No, because the free fall acceleration is constant

for all objects as long as air resistance is negligible.

2) A stone is thrown straight upward with a speed of 20 m/s. a) How high does it go? b) How long does it take to rise to its maximum height? 3) An object is thrown straight upward and falls back to the thrower after a time of 0.80 s. How fast was the object thrown?Answers: 2. (a) d = 20 m. (b) t = 2 s. 3. v1 = 4 m/s

4)A cell phone is thrown downward from the edge of a building with a velocity of 20 m/s and it reached the ground after 4 seconds.

a. Calculate the height of the building.

b. Where will the object be after 2 seconds?

Answers:

(a) 160 m . (b) 80 m above earth, on its way

down.

5) Bobo throws an apple vertically upward from a height of 1.3 m (relative to the ground) with an initial velocity of 4 m/s to a friend on a balcony 3.5 metres above the ground.

a) Will the apple reach this friend?

b) If the apple is not caught, how long

will the apple be in the air before it

hits the ground?

Answer: a. Yes it will, because the maximum heightthe apple can reach is 3.2 m above Bobo’s hand. b. The flying time (up & down) = 1.6 s.

• If an object is moving, there must be a net force making it move.

• Wrong! It could be moving without accelerating.

• Heavy objects must fall faster than light ones.

• Wrong! The rate is the same in vacuum, or when air resistance is negligible (i.e. veryyyyyy small compared to object’s weight).

• When a big object collides with a little one, the big one hits the little one harder than the little one hits the big one.

• Wrong! The 3rd Law says they hit it each other with the same force, but the little object will gain a greater acceleration.

• If an object accelerates, its “speed” must change.

• Wrong! It could be turning at constant speed (i.e. direction changes but not magnitude, so “velocity” is changing) .

Misconceptions

** Normal force• When an object lies on a table or on the

ground, the table or ground must exert an upward force on it, otherwise gravity would accelerate it down.

• This force is called the normal force, and it’s a “contact force” not a “field force” (i.e. it wouldn’t occur unless there is contact between the object and the surface.

In this particular case, N = mg (Newton’s 3rd law).So, Fnet = 0; objects at rest

stays at rest, unless …… ( Newton’s 1st law).

mg

N m

** Normal forces aren’t always vertical

“Normal” means perpendicular. A normal force is always perpendicular to the contact surface.

For example, if a flower pot is setting on an incline, N is not vertical; it’s at a right angle to the incline.

N

mg

Friction

Friction is the force that bodies can exert on each other when they’re in contact.The friction forces are parallel to the contact surfaceand opposite to the direction of motion.

surface

Fr object

v

Friction Facts• Friction is due to electrostatic attraction

between the atoms of the objects in contact.

• It allows you to walk, turn a corner on your bike, and warm your hands in the winter.

• Friction often causes energy waste .

• It makes you push harder and longer to attain a given acceleration.

Friction Example You push a giant barrel on a surface with a constant force (F) of 63 N to the left. If the barrel moved with constant velocity, what is the friction force (Fr )?

Answer: v=constant a=0 Fnet = 0 Fr=F in magnitude and opposite in direction (balanced forces) Fr = 63 N to the right.

F = 63 NBarrel F = 63 N

Suppose you drive a car in a circle at a constant speed.

Even though your speed isn’t changing, you are accelerating.

This is because acceleration is the rate of change of velocity(not speed),

and your velocity is changing because your direction is changing.

This acceleration is called centripetal acceleration.

Circular motion is due to forces acting perpendicular

to the direction of motion,

such forces are called centripetal forces

Centripetal- “Center Seeking” Force

The force that changes the straight path of a particle into a circular or curved path is called the: ‘centripetal force’ or side-way force It is a pull on the body and is directed toward the center of the circle.

Without a centripetal force, an object in motion continues along a straight-line.

With a centripetal force, an object in motion will be accelerated and change its direction.

What is the centripetal force?

Remember Newton’s 1st Law?

Centripetal forcesExamples

1. Friction, as in the turning car example

2. Tension, as in a rock whirling around while attached to a string,

or the tension in the chains on a swing at the park.

Gravity: The force of gravity between the Earth and sun keeps the Earth moving in a nearly circular orbit.

Thank you for watching

Amal Sweis