4 Ch 04 Newton's Laws of Motion and their Applications.pdf

 ( )( ) N20sm80.9kg4005.0 2 ==== mgFf kNkk

( stretch or squish) that produces .

(1) a contact force .

(1) directly and

(1) the velocity of a body is constant, or

(2) has a

(2) has direction opposite from the relative motion

(2) when the body is at rest it is said to be

(3) parallel to the contact surface.

(3) The

(a) horizontally, or

(a) if A rests on B and moves with it (Figure a);

(b) at 30.0° above the horizontal?

(b) if A is held at rest by a string (Figure b).

(c) In part (a), what is the friction force on block A?

(or attempted motion) of the two surfaces in contact.

(or squish) of the spring from its natural unstretched length . The minus sign in Hooke’s law

(You will use such spring

, it is not in equilibrium. The forces acting on it are

. Forces that the object exerts

.astronautOn the

.spacecraftOn the

: exerted by strings, ropes, and wires when they are stretched tight.

: is the force of the earth’s gravitational attraction, which pulls

“external force” exerted on the object

“frictional force”.

“how hard do I push

“how much material

“Mass” is a quantity that obeys the rules of

“To every action there is always opposed an

• A reference frame that moves with constant velocity relative to the distant stars is

• All accelerating reference frames are non-inertial.

• Any reference frame that moves with constant velocity relative to an inertial frame

• Fx = F cos

• Fy = F sin

• In most situations, we shall assume that

• In this case, .

• Inertial frame of reference is an unaccelerated frame.

• Like the previous example, we account for the forces and

• N1, sometimes called the “law of inertia”, defines a special set of reference frames

• SI Units of is kg.m/s 2 =

• The force settings on the spring are calibrated with mass

• The previous example has one new step if the

• The spring scales are often calibrated in force (N) and mass (kg).

• This experiment works in your car, a bus, or even an

• This is a good example of .

• This is a good example of .

• This problem involves two interactive systems in

• We need to be able to find frictional forces given the

• We need to re-examine problems we formerly did as “ideal”.

•If the and the

•The relationship between the force exerted an object

•The so there is no motion.

A block (mass M = 0.25 kg) is at rest on a rough inclined plane (kinetic

a common lab experiment.

A force may be resolved into components – Figure 4.4

A force T is being applied

A free-body-diagram is a diagram that represents

A light spring having a spring constant of k = 125 N/m is used to pull a

A on B B on AF F= −

A penguin slides at a constant velocity of 5.25 m/s down an icy incline.

A surface will always have imperfections, your

A toboggan on a steep hill with friction – Example

a. the distance block A has moved in one second, and

accelerates (changes its state of motion) under the action of

acting on that object. The component of this force that is

acting on the object, not forces the object exerts on its environment.

acting upon it.

actually does occur.

also find that a = 0 and F = 0 for the object.

amusement park ride!

an applied force, i.e.

An example involving two systems – Example

and collect all forces

and frictionless. Find the speed v of mass m when it has fallen distance

and is directed along the + x axis of the coordinate system. If the mass

and the acceleration of that object.

and the astronauts get a (that is, no

and the with each other. 75

another the friction is called static friction.

Application - Example

Application – Example

Application – Example

Applied force, F

are used to represent forces.

arise from physical contact.

b. the distance block B has moved in one second.

balances in some lab

behaviour.

between the sled and the ice is μk = 0.200. If the sled has an acceleration

between two objects.

Block A in the Figure weighs 1.20 N and block B weighs 3.60

bottom of the incline, the penguin slides onto a horizontal patch of ice.

Cables and ropes transmit

called inertial frames. An inertial frame of reference is one in which N1 is valid.

Chapter 1. Introduction and Mathematical Concepts.

Chapter 10. Simple Harmonic Motion and Elasticity.

Chapter 16. Waves and Sound.

Chapter 17. The Principle of Linear Superposition and

Chapter 2. Kinematics in One Dimension.

Chapter 3. Kinematics in Two Dimensions.

Chapter 4. Forces and Newton’s Laws of Motion.

Chapter 5. Dynamics of Uniform Circular Motion.

Chapter 6. Work and Energy.

Chapter 7. Impulse and Momentum.

Chapter 8. Rotational Kinematics.

Chapter 9. Rotational Dynamics.

coefficient of friction μk = 0.35 and angle θ = 30o) and is connected to an

comparing the acceleration of each object produced by a

Consider a spaceship in space and far removed from any planets or other

constructed and calibrated

contact and include gravity and electrical forces.

continue in motion (that is, constant speed

depending on whether they point along the positive or negative x or y axis.

diagram into components that point along these axes.

feel resisting your “push” is the normal force of the table

For two interacting objects A and B, the formal statement of

force are said to obey

force is applied at an angle.

Force x component y component

Forces and free body diagrams: Example

Forces applied at an angle

Forces are applied to both ends of

Forces from static friction increase as force increases while forces

forces through . 13

fourth the weight of block B. Blocks A and C are connected by a

frame (say, one at rest relative to the object) will claim that the acceleration and the

have any value from zero up to a maximum value.

Hooke’s Law (F = ─ k x).

horizontal patch of ice?

How long does the sled take (in seconds) to come to a stop?

How much effort to move the fridge?

If the massless rope passes around a

impending relative motion

in a straight line) unless it experiences a net external force.

In Figure, blocks A and C have the same weight and each weighs one-

In other words: The forces acting on an object in equilibrium must balance.

Individual Forces

Individual Forces

Inertial

Interference Phenomena.

is 40kg. What is the kinetic frictional force?

is a measure of:

is a wonderful example.

is independent of the body’s surroundings and of the

is itself an inertial frame.

is μk = 0.2. After the system is released, [Note that A and B move with

magnitudes and opposite directions. 12

Making only subtle changes in the positions of the apple and the table

Mass is a measure of the amount of “stuff” contained in an object.

massless cord that passes over a massless and frictionless pulley. Assume

Mathematically, the net force is written as

matter. The spaceship requires some propulsion system to “change” its

may be considered massless; and the pulley may be considered massless

Measurement of Force:

method used to measure it.

mitted to the box.

motion and causes the sled to slow down.

motion tend to stay in motion.”

moves and that the coefficient of kinetic friction between blocks A and B

N. The coefficient of kinetic friction between all surfaces is

Newton’s own statement, translated from the Latin of the

on its environment are not included.

parallel to the surface is called the frictional force.

perception of them depends on the magnification.

spacecraft is 11,000 kg and the mass of the astronaut is 92 kg, what are

spaceship reaches a velocity v , the spaceship

Springs that elongate in

ss ff ≤ MAX

standards at normal earth gravity.

Static Region Kinetic Region

Stretch a spring to weigh objects.

Substitution into the second gives

Such springs can be

sum of all of the forces

Suppose that the magnitude of the force is 36 N. If the mass of the

Suppose the coefficient of kinetic friction is μk = 0.05 and the total mass

the best approximation of an inertial frame.

The coefficient of kinetic friction between the penguin and the ice is the

The components are scalar and will be either positive or negative numbers,

the contact area of the surfaces.

the contact force

The direction of the force is such that the string pulls the object to which it is attached.

The first equation gives 21 0.10sin

The force is trans-

The force you

The goal will be to find

The incline slopes above the horizontal at an angle of 15.0°. At the

The is the vector

the magnitude of the force.

The magnitude of the static frictional force can

The net force in this case is: 275 N + 395 N – 560 N = +110 N

The net force ΣF in N2 has components (e.g. in two dimensions): ΣFx and ΣFy

The object and forces

the object toward the earth’s centre. W = mg, m and W are two different quantities.

The on an object is the vector sum of all forces acting on that object.

the overriding principles that give rise to

the rope. These forces have equal

the second body exerts an oppositely directed force

The sled comes to a halt because the kinetic frictional force opposes its

the tabletop as

then a = 0

to drag block B to the left at a constant speed of 2.50 cm/s

to measure the magnitude

to the right end of a rope.

two forces

using the same force.)

velocity of the object remains constant. The

velocity. However, if the propulsion system is turned off when the

Whenever one body exerts a force on a second body,

Whenever two surfaces are in contact they

where the Greek letter sigma denotes the vector sum.

while the acceleration a has components a x and a y. Therefore:

 (This push by the table on your hand is a spring force

 “Objects at rest tend to stay at rest and objects in

 According to N1, a body at rest and one moving with constant velocity are

 An object at rest remains at rest and an object in motion will

 and

 Apply the equations and solve for the unknown quantities.

 Choose a set of x, y axes for each object and resolve all forces in the free-body

 Draw a free-body diagram for each object chosen above. Include only forces

 If you attempt to change the velocity of an object, the

 In one word, we say

 It is the of an object to remain at rest

 Mass and

 Select an object(s) to which the equations of equilibrium are to be applied.

 The “normal force” is

 The “normal force” is the component of the contact force

 The is the vector sum of all of the forces acting on an

 The length of the arrow is proportional to

 Thus, if an object is moving with constant velocity, an observer in one inertial

 What that common statement of the first law often leaves out is the

 When an object is in contact with a surface there is a force

 When the net force on a body is zero , its acceleration is zero.

 When the two surfaces are not sliding across one

As shown in figure,