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Today… Chapter 4. Laws of Motion

Force

Newton’s 1st, 2nd, 3rd laws

Net force

Various Forces

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So far, we learned about

Units, 1d motion, 2d motion, vectors, …

Motivation

Chapter 4: The Laws of Motion

How to describe motions

Chapter 4: The Laws of Motion

Then, what causes the motion ???

What causes an apple to fall?

What causes a ball to undergo projectile motion?

Answer

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Today,

Chapter 4: The Laws of Motion

Forces, Newton’s 1st, 2nd, and 3rd laws

Answer

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ForcesThe measure of interaction between two objects (pull or push). Vector – force has magnitude (unit: N, Newton) and direction

Example F n ppl f m h nd

Force on one object from the other object

Example

Gravitational Force on apple from earth

Force on apple from your hand

apple

Your hand

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Earth

Net ForceNet Force netFIf forces from many objects are applied on a single object

Net force : Vector sum of forces on an object

F n ppl f m h nd

Gravitational Force on apple from earth

Force on apple from your hand

apple

Your handnet on apple hand gravityF F F= +

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Earth

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iClicker Quiz

Two forces of magnitude 5 N are acting on an object.g g jWhat is the magnitude of the net forces?

A) 10 NB) 0 NC) Not enough information

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iClicker Quiz

Two 3N forces are acting on an object.

Which is closest to the magnitude of the net force?

(a) Zero(b) 3.0 N(c) 4 0 N

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(c) 4.0 N(d) 5.0 N(e) 7.0 N

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Example

2 NThree forces are acting on an object.

4 N

90 deg120 deg

+x

+y

3N

Find the net force and its magnitude.

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Newton’s First Law of Motion (The Law of Inertia)

the object at rest remains at rest, the object moving continues to move with the same velocity

(same speed and same direction).

If net force on an object is zero.

If 0, netF = does not change.v

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An additional force is NOT required to keep a cart moving with a constant velocity on a frictionless track!

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iClicker Quiz

1F 2FNot moving

Two forces F1 and F2 are acting on the block as shown above.

Which force has a greater magnitude?

(a) F1

A block is not moving on a frictionless horizontal surface.

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(a) F1

(b) F2(c) They have the same magnitude

iClicker Quiz v = 2.5 m/s

1F 2F

A block is moving to the right at a constant velocity 2.5 m/son a frictionless horizontal surface.

Two forces F1 and F2 are acting on the block as shown above.

While the block is moving at a constant velocity,Which force has a greater magnitude?

(a) F1

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(a) F1

(b) F2(c) They have the same magnitude

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Newton’s Second Law of Motion

• Non-zero net force causes object to accelerate.

If 0, netF ≠ changes, in other words, accelerates.v

• An object of mass m has an acceleration a, equal to the net force F, divided by the mass of the object, m.

netFa =m

netF

netFa =

The acceleration is given by

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am

= m

[ ] [ ] 2

1 1 1

netnet

Fa F mam

mN kg

= ⇒ =

⎡ ⎤= × ⎢ ⎥⎣ ⎦[ ] [ ] 2s⎢ ⎥⎣ ⎦

Newton’s 2nd law in 2 D for each component

2smkg1N1 ≡SI unit of force is a Newton:

Non-SI unit for force: pound (lb) 1 N = 0.225 lb

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, ,; net x x net y yF ma F ma= =Newton’s 2nd law in 2-D for each component

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If the net force acting on an object is in the positive x-direction, the _____ of the object is always in the positive x-direction.

iClicker quiz

y p

(a) displacement (b) velocity(c) acceleration

(d) All of the above(e) None of the above

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In this projectile motion, While the ball is going up, the direction of the net force is

(a)

iClicker

(b)

(c)

(d)

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(e)

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iClicker Quiz

m 5 N4 m/s2

(a) 1 m/s2

(b) 2 m/s2

(c) 4 m/s2

m 10 N a = ?

(c) 4 m/s(d) 8 m/s2

(e) 16 m/s2

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Example v is changing| F2 | = ? N| F1 | = 5 N

A block of mass 4 kg starts from rest and accelerates at a constant rate 5.0 m/s^2 on a frictionless horizontal surface.

Two forces F1 and F2 are acting on the block as shown above.While the block is accelerating,If F1 has a magnitude of 5 N, then the magnitude of F2 is ______ .

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iClciker Q.An object is moving to +x direction at 5 m/s at time t=0.What is the direction of the net force at t=0?

A) +xA) +xB) -xC) Zero magnitude, no directionD) +y or –y directionE) Not enough information

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A car of 1000 kg is moving to +x direction at 8 m/s at time t=0.Later, at time t=2 sec, the car is moving to +x direction at 3 m/s.

What is the direction of the net force on the car between t=0 and

Example

t=2 sec?

Find the net force.

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Equal magnitude and opposite directionAction-reaction pair:

Action and Reaction forces are acting on different objects, NOT on a single object.

Don’t add them to find the net force!!!

Action-reaction versus net force• The 3rd law pair of forces are always applied to different

objects! Net force in Newton’s 1st and 2nd laws is the sum of forces on the

same object.

Ex mpl f ti n & ti nExamples of action & reaction

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Find reaction force for the gravity on the cantaloupe(a) Force on the cantaloupe from the table(b) Gravity force on the earth from the cantaloupe(c) Force on the table from the cantaloupe

iClicker Quiz

(d) Force on the earth from the table(e) Gravity force on the table from the earth

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Next topic..

Various ForcesGravity forceNormal forceTension

Friction forces (static, kinetic)

Motivation

1 2 ...netF F F ma= + + =

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To find the acceleration, we need to add all forces applied to an object of mass m.

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Various Forces

Gravitational Force

Normal Force

Tension Force

Friction Force

Spring Force

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Other forces…

Gravitational Force (Weight):

Magnitude:F h 9 8 / 2

Weight: From the Earth on objects near Earth Surface

F = mg, where g = 9.8 m/s2

•Weight: The force that the Earth is pulling the object with near the surface of the Earth.

Direction: Pointing downward

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A block of mass m is on an inclined surface as below. What is the direction of the gravity force on the block?

(a)

θ

m(b)

(c)

(d)(e)

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(d)

Direction:Direction:

Magnitude:Determined by analyzing forces

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Determined by analyzing forces

From surface on objects in contact

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A block of mass m is on an inclined surface as below. What is the direction of the normal force on the block?

(a)

θ

m(b)

(c)

(d)(e)

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(d)

Example: Person in an elevatorExample: Person in an elevator

A person with a mass 50 Kg in an elevator is moving upward with an upward acceleration 21.1 /a m s=

Identify all forces on the person and find magnitude and direction for each.

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