Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsI

Lecture Capture:

http://echo360.uml.edu/danylov2013/physics1fall.html

Lecture 6

Chapter 4

Dynamics: Newton’s Laws of Motion

09.23.2013 Physics I

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

• Force, Mass

• Newton’s First Law of Motion

• Newton’s Second Law of Motion

• Newton’s Third Law of Motion

• Weight—the Force of Gravity; and the Normal Force/Tension

Outline

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Kinematics to Dynamics

In Kinematics we studied HOW things move

Motion Forces

Motion Forces Now in Dynamics we will study WHY things move

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Force

A force is a push or pull

An object at rest needs a force to get it moving

A moving object needs a force to change its velocity

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Force

Force has magnitude and direction: VECTOR!

Contact forces: exerted by one object in contact with another

Non-contact forces: gravity

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s laws

In 1687 Newton published his three laws in his Principia Mathematica. These intuitive laws are remarkable intellectual achievements and work spectacular for everyday physics

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s 1st Law (Law of Inertia)

In the absence of force, objects continue in their state of rest or of uniform velocity in a straight line

i.e. objects want to keep on doing what they are already doing

It helps to find inertial reference frames

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Inertial reference frame

An inertial reference frame is one in which Newton’s first law is valid.

This excludes rotating and accelerating frames (non-inertial reference frames), where Newton’s first law does not hold.

How can we tell if we are in an inertial reference frame? By checking to see if Newton’s first law holds!

Inertial reference frame – A reference frame at rest – Or one that moves with a constant velocity

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s Second Law of Motion

Newton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass.

amF =

2smkgN ⋅=

New unit of force Newton

It takes a force to change either the direction or the speed of an object. More force means more acceleration; the same force exerted on a more massive object will yield less acceleration.

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Mass

Mass is the measure of inertia of an object, sometimes understood as the quantity of matter in the object. In the SI system, mass is measured in kilograms.

Mass is not weight.

Mass is a property of an object. Weight is the force exerted on that object by gravity.

If you go to the Moon (gravitational acceleration is about 1/6 g), you will weigh much less. Your mass, however, will be the same.

amF = Proportionality defines mass of object.

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s 2nd Law. Example 4-2

Estimate the net force needed to accelerate a 1000-kg car at 5m/s2;

�𝐹 = ma ≈ (1000 kg)(5 𝑚/𝑠2)=5000 N

m=1000 kg

a=5 m/s2

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Example 4-3 Force to stop a car.

What average net force is required to bring a 1000-kg car to rest from a speed of 20 m/s within a distance of 100 m?

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s 3rd Laws

• But where do forces on an object come from? • Forces come from other objects

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s Third Law of Motion

Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.

“For every action force, there is an equal and opposite reaction force” NOTE: Action and Reaction forces act on different objects!

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s 3rd Law

When a hammer hits a nail, the hammer stops very quickly

i.e. the hammer changes velocity, i.e. it decelerates (a)

So, nail must also exert a Force on the hammer (F=ma).

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Action-Reaction Forces

A key to the correct application of the third law is that the forces are exerted on different objects.

Make sure you don’t use them as if they were acting on the same object.

Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source.

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Newton’s Third Law of Motion Rocket propulsion can also be explained using Newton’s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket.

Hero’s engine - water-propelled engine from a soft drink cans. Water flowing out of holes in the can cause the can to rotate in the direction opposite to the stream, explained by Newton's Third Law of motion.

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

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Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Weight—the Force of Gravity

Weight is the force exerted on an object by gravity.

all objects dropped near the surface of the Earth accelerates with g towards Earth.

amF =Newton’s 2nd Law

On earth’s surface

Force of gravity (weight)

Non-contact force

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

When you solve problems using forces…

• Need to decide motion of which object we want to describe

• To find motion of an object,

need to know forces acting ON that object

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Reaction Forces: “Normal” Force

An object at rest must have no net force on it. If it is standing on a ground, the force of gravity is still there; what other force is there?

The force exerted perpendicular to a surface is called the normal force, .

It is exactly as large as needed to balance the force from the object.

FG

FN

��⃗� = 𝑚�⃗�

𝐹𝐺 − 𝐹𝑁=0

= 0

𝐹𝑁 = 𝐹𝐺

FN

y

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Determine the normal force exerted on the box by the table.

Use Newton’s 2nd Law y 𝑭𝑵

m𝒈

��⃗� = 𝑚�⃗�

𝐹𝑁 − mg = 0

a= 0 (no motion)

y 𝑭𝑵

m𝒈

40N

��⃗� = 𝑚�⃗�

𝐹𝑁 −𝑚𝑚 − 40𝑁 = 0

𝐹𝑁 = 𝑚𝑚 + 40𝑁

a= 0 (no motion)

𝐹𝑁 = mg

The normal force is greater

Box is a described object

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Use Newton’s 2nd Law

y

𝑭𝑵

m𝒈

��⃗� = 𝑚�⃗�

𝐹𝑁 −𝑚𝑚 40𝑁 = 0

a= 0 No motion

𝐹𝑁 = 𝑚𝑚 − 40𝑁

+

The normal force is smaller

Determine the normal force exerted on the box by the table.

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

A 65-kg woman descends in an elevator that briefly accelerates at 0.20g downward. She stands on a scale that reads in kg. What does the scale read?

y

��⃗� = 𝑚�⃗� m𝒈

𝑭𝑵

Example 4-8: Apparent weight loss.

𝑚𝑚 𝐹𝑁 = 𝑚𝑎 Y direction −

𝑎 = 0.2𝑚 𝐹𝑁 = 𝑚𝑚 −𝑚𝑎 = 𝑚(𝑚 − 𝑎) = 𝑚(𝑚 − 0.2𝑚) = 0.8𝑚𝑚

Although her weight is still mg, the scale would read less, 0.8mg

Woman is a described object

The block is moving at constant speed, so

it must have no net force on it. The forces

on it are N (up) and mg (down), so N = mg,

just like the block at rest on a table.

ConcepTest 1 Going Up I A block of mass m rests on the floor of

an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block?

A) N > mg

B) N = mg

C) N < mg (but not zero)

D) N = 0

E) depends on the size of the elevator

m

v

𝑚𝑚 − 𝐹𝑁 = 𝑚𝑎 v=const a= 0

𝐹𝑁 = 𝑚𝑚

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Reaction Forces: Tension If a flexible cord pulls an object, the cord is

said to be under TENSION

Ft1 Ft2 m

��⃗� = 𝑚�⃗� 𝐹𝑡𝑡 − 𝐹𝑡2

𝑚=0 (assume, the mass of the cord is negligible) 𝐹𝑡2 = 𝐹𝑡𝑡 = 𝐹𝑡

𝐼𝐼 𝑤𝑤 𝑎𝑎𝑎𝑎𝑎 𝑎 𝐼𝑓𝑓𝑓𝑤 𝑡𝑓 𝑓𝑜𝑤 𝑤𝑜𝑒 𝑓𝐼 𝑡𝑡𝑤 𝑓𝑓𝑓𝑒, 𝑡𝑡𝑤 𝑠𝑎𝑚𝑤 𝐼𝑓𝑓𝑓𝑤 𝑤𝑤𝑎𝑎 𝑏𝑤 𝑓𝑜 𝑡𝑡𝑤 𝑓𝑡𝑡𝑤𝑓 𝑤𝑜𝑒

= 𝑚𝑎 =0 Cord is a described

object

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

ConceptTest 2. Tension

Ft

Ft

Ft Ft

ceiling

wall Fwc=Ft

The tension in the rope is Ft in all of the above

Which situation gives us the largest rope tension?

(A)

(B)

(C)

(D) Tensions are equal.

Fcw=Ft

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

Thank you See you on Wednesday

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

ConceptTest 3 : Weights 1

ceiling A 1-kg mass hangs on a spring scale attached to the ceiling. What is the reading on the spring scale (rounded to the nearest Newton)?

(A)Zero

(B)1 Newton

(C) 10 Newtons

(D) 20 Newtons

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

ConceptTest 4: Weights 2

wall

A 1-kg mass is attached to a spring scale as shown. What is the reading on the spring scale (rounded to the nearest Newton)?

(A)Zero

(B)1 Newton

(C) 10 Newtons

(D) 20 Newtons

Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 6

ConceptTest 5 : Weights 3

Two 1-kg masses are attached to a spring scale as shown. What is the reading on the spring scale (rounded to the nearest Newton)?

(A)Zero

(B)1 Newton

(C) 2 Newtons

(D) 10 Newtons

(E) 20 Newtons

The block is accelerating upward, so

it must have a net upward force. The

forces on it are N (up) and mg (down),

so N must be greater than mg in order

to give the net upward force!

1) N > mg

2) N = mg

3) N < mg (but not zero)

4) N = 0

5) depends on the size of the elevator

Σ F = N – mg = ma > 0 ∴ N > mg

m a > 0

mg

N

A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block?

ConcepTest 7 Going Up II

Follow-up: What is the normal force if the elevator is in free fall downward?

When the fly hit the truck, it exerted a force on the truck (only for a fraction of a second). So, in this time period, the truck accelerated (backward) up to some speed. After the fly was squashed, it no longer exerted a force, and the truck simply continued moving at constant speed.

ConcepTest 8 Truck on Frozen Lake A very large truck sits on a

frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck?

1) it is too heavy, so it just sits there 2) it moves backward at constant

speed 3) it accelerates backward 4) it moves forward at constant speed 5) it accelerates forward