PHY115 – Sault College – Bazlurslide 1 Newton’s Second Law of Motion

PHY115 – Sault College – Bazlur slide 1

Newton’s Second Law of Motion


Newton’s Laws of Motion1. Newton’s First Law of Motion

– Every object will continue in a state of rest or with constant speed in a straight line unless acted upon by an external force.

2. Newton’s Second Law of Motion – When a net force act on an object, the object accelerates

in the direction of the net force. The acceleration is directly proportional to the net force and inversely proportional to the mass. Thus, a F/m or, a F/m

3. Newton’s Third Law of Motion – Whenever one object exerts a force on a second object,

the second object exerts an equal and opposite force on the first.


Cause of Acceleration: ForceForce causes acceleration

When you apply a force on a hockey puck and it starts to move – it accelerates.

When the hockey is no longer pushing it, the puck moves at constant velocity, unless any other force acting on it.

To increase the acceleration, you must increase the net force acting on it.

Acceleration net force

If you double the net force, its acceleration doubles.



To increase the acceleration, you must increase the net force acting on it.


a F

If you double the net force, its acceleration doubles.


Acceleration due to net forcea = F / m

2a = 2F / m

a = 2F / 2m

a = F / m


Friction reduces the net force When surfaces slide or tend to slide over one

another, a force of friction acts.

When you apply a force to an object, a force of friction usually reduces the net force and the resulting acceleration.


FrictionFriction is caused by

– the irregularities in the surfaces in mutual contact, and

– depends on the kinds of material and – how much they are pressed together.

Even surfaces that appear to be very smooth have microscopic irregularities that obstruct motion.

Atoms cling together at many points of contact. When one object slides against another, it must either rise over the irregular bumps or else scrape atoms off.

Either way requires force.


FrictionThe direction of the friction force is always in a

direction opposing motion.

– An object that slides to the right experiences friction toward the left;

– The sack falls downward, and air friction acts upward;

– An object sliding down an incline experiences friction directed up the incline;


FrictionThe direction of the friction force is always in a

direction opposing motion.

Thus, if an object is to move at constant velocity, a force equal to the opposing force of friction must be applied so that the two forces exactly cancel each other.

The zero net force then results in zero acceleration.


Friction does not depend on areaFriction depends on the force of contact between the two

surfaces, which is usually caused by gravity (in other words, the object's weight). Not the surface area.

If you have a large area of contact, the weight of the object is distributed more, and so any specific point has less pushing down on it. With a small area of contact, each point on the area of contact bears more weight. So if you have a greater area of contact, it would make sense that there is more friction, but since the weight is distributed over a wider surface, they cancel each other out, and only the force of contact matters.

So, extra sand bags (weight) help in the winter.

Air resistance, however, is an example of a friction force that 'does' depend on the area of contact, and the formula for air resistance includes speed and area, a totally different formula than most friction equations.


Fluid FrictionFriction is not restricted to solids sliding over one another. Friction occurs also in

liquids and gases, collectively called fluids (because they flow).

Fluid friction is called drag.

Just as the friction between solid surfaces depends on the nature of the surfaces, drag in a fluid depends on the nature of the fluid; for example, drag is greater in water than it is in air.

But unlike the friction between solid surfaces, such as the crate sliding across the floor, drag does depend on speed and area of contact.

This makes sense, for the amount of fluid pushed aside by a boat or airplane depends on the size and the shape of the craft. A slow-moving boat or airplane encounters less drag than faster boats or airplanes. And wide boats and airplanes must push aside more fluid than narrow crafts.

For slow motion through water, drag is approximately proportional to the speed of the object.

In air, drag at most speeds is proportional to the square of the speed. So if an airplane doubles its speed it encounters four times as much drag. At very high speed, however, the simple rules break down when the fluid flow becomes erratic and such things as vortices and shock waves develop.


Equation of Friction• The classical approximation of the force of friction known as

Coulomb friction (named after Charles-Augustin de Coulomb) is expressed as:

Ff = μN, – where μ is the coefficient of friction, N is the force normal to the

contact surface, and Ff is the force exerted by friction. This force is exerted in the direction opposite the object's motion.

• This law mathematically follows from the fact that contacting surfaces have atomically close contacts only over extremely small fraction of their overall surface area, and this contact area is proportional to load (until saturation takes place when all area is in atomic contact thus no further increase of friction force takes place).

• http://en.wikipedia.org/wiki/Friction


Types of friction • Static friction - is the friction acting on a body when the body

is not in motion, but when a force is acting on it. – If there is no force, no friction.– Limiting friction - is the friction on a body just before it starts moving.

Generally, limiting friction is highest.

• Kinetic friction - is the friction which acts on the body when the body is moving. Kinetic friction is usually smaller.

– Sliding - is when two objects are rubbing against each other. Putting a book flat on a desk and moving it around is an example of sliding friction

– Fluid - is the friction between a solid object as it moves through a liquid or a gas.

• depend on the speed and

• depend on the area of contact.


Mass opposes Acceleration The acceleration imparted to an object depends not only

on applied forces and friction forces, but also on the inertia of the object.

How much inertia an object possesses depends on the amount of matter in the object—the more matter, the more inertia.

In speaking of how much matter something has, we use the term mass.

The greater the mass of an object, the greater its inertia.

Mass is a measure of the inertia of a material object.


Mass vs. Weight Mass: The quantity of matter in an object.

It is also the measure of the inertia or sluggishness that an object exhibits in response to any effort made to start it, stop it, or change its state of motion in any way.

Weight: The force upon an object due to gravity.


Mass vs. WeightIn the United States, the quantity of matter in an object is commonly described by the gravitational

pull between it and the Earth, or its weight, usually expressed in pounds.

In most of the world, however, the measure of matter is commonly expressed in a mass unit, the kilogram. At the surface of the Earth, a brick with a mass of 1 kilogram weighs 2.2 pounds. In metric units the unit of force is the newton, which is equal to a little less than a quarter-pound (like the weight of a quarter-pounder hamburger after it is cooked). A 1-kilogram brick weighs about 10 newtons (more precisely, 9.8 N).

Away from the Earth's surface, where the influence of gravity is less, a 1-kilogram brick weighs less. It would also weigh less on the surface of planets with less gravity than the Earth. On the moon's surface, for example, where the gravitational force on things is only 1/6 as strong as on Earth, a 1-kilogram object weighs about 1.6 newtons (or 0.36 pound). On planets with stronger gravity it would weigh more.

But, the mass of the brick is the same everywhere. The brick offers the same resistance to speeding up or slowing down regardless of whether it's on the Earth, moon, or any body attracting it. In a drifting spaceship where a scale with a brick on it reads zero, the brick still has mass. Even though it doesn't press down on the scale, the brick has the same resistance to a change in motion as it has on the Earth.

Just as much force would have to be exerted by an astronaut in the spaceship to shake the brick back and forth as would be required to shake it back and forth while on Earth. You'd have to provide the same amount of push to accelerate a huge truck to a given speed on a level surface on the moon as on Earth. The difficulty of lifting it against gravity (weight), however, is something else. Mass and weight are different from each other (Figures 4.5 and 4.6).


Mass vs. WeightAn anvil in outer space, between the Earth and moon for

example, may be weightless, but it is not massless.

The astronaut in space finds it is just as difficult to shake the “weightless” anvil as it would be on Earth.


Mass vs. WeightA nice demonstration that distinguishes mass

and weight is the massive ball suspended on the string, shown in Figure.

The top string breaks when the lower string is pulled with a gradual increase in force, but the bottom string breaks when the string is jerked. Which of these cases illustrates the weight of the ball, and which illustrates the mass of the ball?

Note that only the top string bears the weight of the ball. So when the lower string is gradually pulled, the tension supplied by the pull is transmitted to the top string. So total tension in the top string is pull + weight of the ball. The top string breaks when the breaking point is reached.

But when the bottom string is jerked, the mass of the ball - its tendency to remain at rest - is responsible for the bottom string breaking.


newton, the unit of force • The newton (symbol: N) is the SI unit of force.

• It is named after Sir Isaac Newton.

• A newton is the amount of force required to accelerate a mass of one kilogram by one metre per second squared.

http://en.wikipedia.org/wiki/Newton


Weight Weight: The force upon an object due to gravity.

F = ma

W = mgW, is the force due to gravity

g, is the acceleration due to gravity

Weight of an object of mass 1kg is

W = mg

= 1kg x 9.8 m/s2

= 9.8 N

10 N


Pounds? • In the USCS system of units, both force and

mass are called pounds.

Mass, 1 kg = 2.2 lb

Weight, 9.8 N = 2.2 lb

• Therefore, one must distinguish the pound-force (lbf) from the pound-mass (lbm).

Mass, 1 kg = 2.2 lbm

Weight, 9.8 N = 2.2 lbf

• The pound-force is that force which accelerates one pound-mass at 32.174 ft/s2.

• Thus, 1 lbf = 32.174 lbm-ft/s2.


Slug, unit of mass in fps system • It is a mass that accelerates by 1 ft/s² when a

force of one pound-force (lbf) is exerted on it.

F = ma

1 lbf = 1 slug x 1 ft/s2

1 lbf = 32.174 lbm-ft/s2

• So, 1 slug = 32.174 lbm = 14.593 kg

• Therefore a slug has a mass of about 14.593 90 kg and weighs approximately 32.174 05 pounds.

• Another name for this unit in early literature is the geepound.


Mass Resists Acceleration Push your friend on a skateboard and your friend accelerates.

Now push equally hard on an elephant on the skateboard and acceleration is much less.


Mass Resists Acceleration You'll see that the amount of

acceleration depends not only on the force, but on the mass being pushed.

– The same force applied to twice the mass produces half the acceleration.

– For three times the mass, one-third the acceleration.


Mass Resists Acceleration We say that for a given force, the

acceleration produced is inversely proportional to the mass.

That is, By inversely we mean that the two values change in opposite directions.

As the denominator increases, the whole quantity decreases. For example, the quantity is less than .

1/10 > 1/100


Newton's Second Law of Motion The relationship of acceleration to force and inertia is

given in Newton's second law.

The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.


Newton’s Second Law Although Galileo founded both the concepts of

inertia and acceleration, and was the first to measure the acceleration of falling objects,

Galileo could not explain why objects of various masses fall with equal accelerations.

Newton's second law provides the explanation.


When Acceleration is g, it is Free Fall We know that a falling object accelerates toward

the Earth because of the gravitational force of attraction between the object and the Earth.

When the force of gravity is the only force—that is, when friction such as air resistance is negligible— we say that the object is in a state of free fall.


Gravitational Acceleration g, is constantSo twice the force exerted on

twice the inertia produces the same acceleration as half the force exerted on half the inertia.

Both accelerate equally.

The ratio of weight (F) to mass (m) for freely falling objects equals a constant, g.

The acceleration of free fall is independent of an object's mass.


When Acceleration Is Less Than g, Nonfree Fall

In a vacuum or in cases where air resistance can be neglected, the net force is the weight because it is the only force.

In the presence of air resistance, however, the net force is less than the weight—it is the weight minus air drag, the force arising from air resistance.

So, the acceleration is smaller than compared to freefall.


Air Drag The force of air drag experienced by a falling object

depends on two things.

First, it depends on the frontal area of the falling object—that is, on the amount of air the object must plow through as it falls.

Second, it depends on the speed of the falling object; the greater the speed, the greater the number of air molecules an object encounters per second and the greater the force of molecular impact.

Air drag depends on the size and the speed of a falling object.


Terminal velocityIn some cases air drag greatly affects falling; in other cases it

doesn't.

Air drag is important for a falling feather.

Since a feather has so much area compared to its small weight, it doesn't have to fall very fast before the upward-acting air drag cancels the downward-acting weight.

The net force on the feather is then zero and acceleration terminates.

When acceleration terminates, we say the object has reached its terminal speed.

If we are concerned with direction, down for falling objects, we say the object has reached its terminal velocity.

The same idea applies to all objects falling in air.


Terminal velocityFor a feather, terminal velocity is a few

centimeters per second,

whereas for a skydiver it is about 200 kilometers per hour.


Terminal velocityWho gets to the ground first

– the heavy man or – the lighter woman?


Terminal velocityWho gets to the ground first

– the heavy man or – the lighter woman?


Acceleration? A skydiver jumps from a high-flying helicopter. As

she falls faster and faster through the air, does her acceleration increase, decrease, or remain the same?


Acceleration?Acceleration decreases because the net force on her

decreases.

Net force is equal to her weight minus her air resistance, and since air resistance increases with increasing speed, net force and hence acceleration decrease.

By Newton's second law, where mg is her weight and R is the air resistance she encounters.

As R increases, a decreases.

a = Fnet / m

= (mg – R) /m


What velocity? A skydiver jumps from a high-flying helicopter. As

she falls faster and faster through the air, does her acceleration increase, decrease, or remain the same?

What happens to the velocity when acceleration terminates?


What velocity? Note that if she falls fast enough so that R = mg, a = 0,

then with no acceleration she falls at constant speed.

She reached her terminal velocity, a constant velocity.

Documents

PHY115 – Sault College – Bazlurslide 1 Newton’s Second Law of Motion