Fascinating Education Script
Fascinating Physics Lessons
Lesson 3: Forces
Slide 1: Introduction
Slide 2: An object in motion, stays in motion.
It’s been known since the time of Galileo in the 16th century that once an object is pushed or
pulled into motion, it will remain in motion forever.
You don’t need to keep adding energy to a moving
object in order to keep it moving. All a force has to do
is accelerate the object to some velocity, and the
object will continue in that direction and speed, until
another force changes its direction, or its speed, or
both.
Sir Isaac Newton formalized this principle, so it’s
called Newton’s first law. The tendency for a
stationary object to remain in a stationary position, or
a moving object to keep moving, is called “inertia.”
Slide 3: Newton’s second law: force equals mass times acceleration.
Obviously, it takes more force to get a heavy object
moving than it does a light object. Sir Isaac Newton
summarized this in a formula known as Newton’s
second law: force equals mass times acceleration.
This formula says that if you apply a force to a mass,
the mass will accelerate. This formula also says that
if you increase the size of the mass, it will take more
force to get the same acceleration. We’ve all
experienced this.
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It takes more force to lift a heavy object and overcome the force of gravity than it does to lift a
light object.
Slide 4: What about in outer space where there is no gravity?
What about in outer space, where for all intents and
purposes, there is no gravity?
Is it more difficult to lift a heavy object than a light one?
Yes, but how could that be?
How could it be more difficult to lift a heavy object than a
light one where objects have no weight?
Slide 5: Larger masses have more inertia.
You don’t lift an object in outer space. You move it, and it takes more force to move a large
mass than a small one.
You don’t have to go to outer space to observe this. Try
moving a bowling ball resting on a table top. Getting the
ball to roll does not require overcoming the force of
gravity. Yet you know that it takes more force to move a
heavy bowling ball sideways than it does a lighter
bowling ball.
Does it take the same amount of force to lift the bowling
ball off the table as it does to get it rolling? No. Lifting
requires you to also overcome the force of gravity pulling the ball downward. Rolling the ball
does not.
Yes, the bowling ball is heavy, but that’s not why it takes so much force to get it rolling. The
property of the bowling ball that resists being moved is its mass. Larger masses have more
inertia – more resistance to being moved.
Slide 6: Newton’s formula
Newton’s formula -- force equals mass times acceleration – says that the amount of force
needed to accelerate a mass, that is, to change its speed or direction of movement, depends on
its mass, not its weight. Weight is a downward force equal to mass times the acceleration of
gravity: mass times g.
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If something weighs 100 kg, that means the object is
being pulled toward the center of the earth with a force
equal to the mass of the object times the acceleration of
gravity. That force is called weight.
In everyday speech, we say that an object’s weight is 100
kg, even though that’s really its mass. We should be
saying that an object’s weight is its mass, 100 kg, times
the acceleration of gravity, 9.81 meters per second
squared, in other words, 981 newtons, which is the unit
for force.
However, for things sitting on the surface of the earth, mass and weight are often used
interchangeably, even though they shouldn’t be. In doing physics problems, be careful when
the problems states that the weight of the object is 100.0 lbs, because its mass is only 100 lbs
divided by the acceleration of gravity, 32 feet per second squared.
The unit of weight in the metric system is newtons, which is units of force, in this case the force
of gravity on the mass.
When pushing a mass horizontally along a frictionless surface, the downward force of gravity,
mg, doesn’t alter how fast the object accelerates when pushed. Only the mass of the object
matters. That’s because the mg vector is pointing downward, perpendicular to the direction of
movement. None of the downward force is opposing the force pushing the mass along the
frictionless surface.
In weightless space where there is minimal gravity, Newton’s formula, force equals mass times
acceleration, says that in order for two different sized masses to be accelerated equally, you
have to exert more force for the bigger mass. This is because acceleration is force divided by
mass. The bigger the mass, the more force needed to get the same acceleration.
This property of all masses, namely, that larger masses need more force to change their speed
or direction, is called inertia. Inertia only depends on mass: the larger the mass, the more
inertia the mass has, and the more force it takes to accelerate the mass from its current path.
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Slide 7: How can a heavy boulder and a small stone fall at the same rate?
When dropped from the St. Louis arch, a heavy
boulder and a small stone fall at the same rate and
strike the ground at the same time. This means that
they both accelerated at the same rate from a resting
position, which, in turn, means that the force moving
the boulder divided by the mass of the boulder had
to be the same as the force moving the stone divided
by the mass of the stone. Despite the larger force
needed to get the boulder moving, the heavy
boulder and the smaller stone have the same
acceleration.
Slide 8: Mass is not the same as weight.
Mass is not the same as weight. Weight is the effect of gravity acting on a mass. You have to
exert more force to overcome the force of gravity for an object sitting on the earth’s surface
than the same object 5000 feet above the earth where gravity is weaker.
Deep in the interior of the earth, the mass of an
object is the same, but its weight is less, because the
force of gravity pulling the mass toward the center of
the earth is now being offset by the force of gravity
being exerted by all the earth sitting above the mass.
What is the force needed to accelerate a 1 kg mass to
1 meter per second squared? The force would be 1
kg-meter per second squared. This cumbersome set
of units was condensed into a single Newton, after Sir
Isaac Newton. The units for force, then, are Newtons.
𝑓𝑜𝑟𝑐𝑒 = 1 𝑘𝑔 𝑥 1
𝑚
= 1 𝑘𝑔 𝑚/𝑠𝑒𝑐 2 = 1 𝑁𝑒𝑤𝑡𝑜𝑛
𝑠𝑒𝑐 2
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Slide 9: Newton’s third law
Newton’s second law says that if you exert a force on a
stationary mass, the mass will move. But when gravity
exerts a downward force on this teddy bear sitting on a
table top, the teddy bear doesn’t move downward. The
only explanation is that the table top must be exerting a
force equal to gravity in an upward direction.
Otherwise, the teddy bear would be moving.
So if you know that an object is being pulled or pushed
in one direction, but isn’t moving, it must be
experiencing an equal force in the opposite direction.
This is Newton’s third law.
Slide 10: Using sines and cosines
Here is a 10.0 kg light fixture hung off center. On one
side, it forms an angle of 35.0 degrees with the ceiling,
and on the other side 65.0 degrees. The fact that the
light fixture is not moving means that the forces trying to
move it sideways and up and down must be offsetting
each other. Knowing that, and knowing that the fixture
weighs 10.0 kg, how strong does the wire have to be to
hold up the light fixture? How much force must the wire
be able to withstand before it snaps?
First, think about the forces pulling the light fixture in the X and Y directions. Both diagonal
wires are exerting a force in both the X and Y direction, and by using sines and cosines, we can
figure out the component of force along the X and Y axes. The two X components have to offset
each other because they are pulling in opposite directions and the light fixture is not moving
sideways.
The two Y components, however, are both pulling in the same direction – upward -- and yet the
fixture is not moving. There must be another force pulling the fixture downward. Of course, the
force of gravity, m times g, the weight of the light fixture. This downward force has to equal the
combined upward components exerted by the force of the wires. We now have two equations
for the two unknown forces, F1 and F2.
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Slide 11: Solve the problem.
Here are the two equations for F1 and F2. Along the X axis, the leftward force of F1 times the
cosine of 35 degrees equals the rightward force of F2 times the cosine of 65 degrees.
Along the Y axis, the upward force of F1 times the sine of 35 degrees plus the upward force of
F2 times the sine of 65 degrees equal the downward force of gravity being exerted on the 10
kilogram chandelier.
Let's solve for F1 along the x axis. F1 equals 0.51 times
F2. Substituting the value of F1 into the equation for
forces exerted in the Y direction, we get the values for
F1 and F2.
The force exerted by the shorter section of the wire is
81.8 newtons, while the force exerted by the longer
section is only 0.51 of this, or 41.7 newtons. The wire
must be able to withstand 81.8 newtons of force.
Slide 12: How does a rocket engine propel a rocket forward?
How does a rocket engine propel a rocket forward, if
the gas coming out the back of the engine meets so
little resistance from the air? Where does the opposite
and equal force come from to propel the rocket
forward? From the gas molecules themselves. The hot
gas molecules don’t need to exert their force against a
rigid surface. Newton’s third law says that exerting a
force in one direction automatically exerts an equal and
opposite force in the opposite direction – in this case,
forward, which sends the rocket on its way.
Slide 13: Catching our breath
Let’s stop here and catch our breath.
Newton provided us with three laws of motion. His first law said that unless an object is
experiencing a force at this moment, it will continue doing what it was doing. The reason things
slow down is that another force, typically the force of friction, acts on the object to slow it
down. The resting state occurs, then, whenever there is no force acting on the object. If the
object is already moving, and there is no fraction to stop it from moving, the object will
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continue moving forever. The flip side of Newton’s first law is that in order to accelerate an
object from its resting state, in other words, to change its current velocity -- its speed or
direction -- a force must be applied.
Newton’s second law states that the magnitude of the
force needed to change a mass’ velocity depends on
the magnitude of the mass, and the magnitude of the
acceleration you to want to apply. He summarized this
concept with the formula: force equals mass times
acceleration. Mass, then, could be thought of as the
resistance an object puts up when a force tries to
change its’ current speed or direction.
Newton’s third law is that for every action, there is an equal and opposite reaction. So if an
object is not moving, look above and below the object, to its left and to its right, and in front of
and behind it, because if it’s not moving, there is either no force acting from any of those
directions, or there is a force, but that’s being opposed by an equal and opposite force from the
opposite direction.
And don’t forget that forces are vectors that cast shadows, meaning that if the direction of a
force vector is not exactly along the X and Y axes, you will likely have to lay down a set of X and
Y axes at the back end of the vector, and analyze its shadows along the X and Y axes using sines,
cosines, and tangents.
Slide 14: Friction is determined by two factors.
Pushing a block across a table requires overcoming
friction between the block and the table. Friction is
determined by two major factors. One is the nature of
the surfaces -- the smoothness of the block and the
smoothness of the table, and the chemical attraction
between molecules along the surfaces of the block and
the table. The other determinant of friction is the weight
of the block being moved. The heavier the block, the
more the block and table are squeezed together, which
increases the friction. The force pushing the two
surfaces together is always perpendicular to the surfaces. This force is called the normal force.
For an object sitting on a horizontal surface, the normal force is simply the force of gravity:
mass times the acceleration of gravity.
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The force of friction is the normal force, in this case, mass times the acceleration of gravity,
multiplied by a number that takes into consideration the roughness and the chemistry of the
surfaces. This number, called the coefficient of friction and symbolized by the Greek letter mu,
has no units. It is simply a number. Typical coefficients of friction for stationary objects include
rubber on concrete, a husky 0.75; wood on concrete: 0.62; and Teflon on steel, a measly 0.04.
The force of friction opposes any force trying to move the object, so the direction of the friction
vector is opposite to the direction of movement. Until the object moves, the force of friction
equals the force trying to move the object.
Slide 15: The force of friction prevents and object from moving.
The force of friction prevents an object from moving when the object is first pushed or pulled.
As more and more force is applied, the friction force also increases to match the applied force -until the applied force is strong enough to overcome the force of friction. The maximal force of
friction preventing the object from moving is called the force of static friction. Once the applied
force equals the force of static friction, the block begins to move.
The force of static friction is the normal force – the mass
of the object times the acceleration of gravity times mu,
the coefficient of static friction.
Steel on steel has a coefficient of friction of 0.74. How
much horizontal force will it take to get this steel box
weighing 25.0 kg to slide along a steel table?
It will take enough force to overcome the force of static
friction. The force of static friction is mg times mu, or
25.0 kg x 9.81 meters per second squared, times 0.74, the coefficient of steel on steel, or 181.5
newtons of force. The force of static friction is 181.5 newtons, so it will take 181.5 newtons to
get the steel box moving.
Slide 16: The force of static friction
If a cable attached to a 15.0 kg wooden box at an angle of 35 degrees exerts a force of 105.0
newtons, what is the acceleration of the box at the moment it begins to move?
The coefficient of static friction between the wooden box and the concrete is 0.62.
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At the moment the box begins to move, the force of static friction opposing its movement is the
normal force pushing down on the box times the coefficient of static friction. The normal force
cannot simply be mg, because some of the force exerted along the cable is lifting the box, and
we have to subtract that upward component.
The net normal force, then, is the mass of the box times
the acceleration of gravity minus the upward lift from
the cable. The upward lift from the cable is the
hypotenuse, 105.0 newtons, times the sine of 35
degrees.
The net normal force is 15.0 kg x 9.81 meters per second
squared minus 105.0 newtons times the sine of 35
degrees, which calculates out to be 87.3 newtons.
The net normal force of 87.3 newtons is then multiplied by mu, the coefficient of static friction,
to get the force of static friction at the moment the box starts moving. 87.3 newtons times 0.62
is 54.1 newtons.
At the moment the box starts moving, the net force pulling the box horizontally is the force
exerted by the cable in the X direction minus the force of static friction.
105 N x cos 35o – 54.1 N = 86.1 N – 54.1 N = 32.0 N
Since force equals mass times acceleration, 32 newtons of force equals 15 kilograms times its
acceleration. The box accelerates at 2.1 meters per seconds squared.
Slide 17: Two types of friction
Once an object is pushed with enough force to get it moving, the friction changes from static
friction before it moved, to kinetic friction after it
moved. Because there are two types of friction, there
are also two coefficients of friction: one that measures
the friction between two objects at rest, and another
for two objects sliding past each other. As you might
imagine, the friction between two objects sliding past
each other is lower than between two stationary
objects, because once all the chemical bonds holding
two stationary objects together are broken, the two
objects have an easier time sliding past one another.
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That’s why you don’t want to press too hard on the brakes in wet or icy conditions. Once the
car starts to slide, the lower coefficient of kinetic friction allows the car to continue sliding out
of control.
Slide 18: Normal force
At the moment the box began to move, the force
necessary to overcome static friction and get the box
moving was the normal force – the mass of the box
times the acceleration of gravity -- times mu, the
coefficient of static friction.
This force minus the force of kinetic friction then
accelerates the box according to the usual formula of
mass times acceleration.
If the force of kinetic friction is small, then the force that overcame the force of static friction is
the same force that is now accelerating the box. M times g times mu equals mass times
acceleration. The masses cancel out, and the acceleration of gravity times mu equals the
acceleration of the box.
What does all this mean in English? It means that the weight of the object has no bearing on
how fast it accelerates from a stationary position. At the moment the force is able to overcome
the force of static friction, a heavy object accelerates at the same rate as a light object if the
surface is smooth enough.
The reason a heavier object accelerates at the same rate as a lighter object is that while a
heavier object takes more force to get it moving, this stronger force is able to accelerate the
heavier object at the same rate as the smaller force accelerating the lighter object.
That’s why the boulder and stone fell from the St. Louis arch at the same acceleration.
Slide 19: What is the magnitude of the normal
force?
When an object is on an incline, it will not slide unless
the force pushing it down the incline exceeds the force
of static friction. The force of static friction is the normal
force pushing the two surfaces together times the
coefficient of static friction.
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The normal force pushing the two surfaces together is directed perpendicular to the surfaces.
But what is the magnitude of the normal force? That is, what is the length of the normal force
vector?
On an incline, the magnitude of the normal force cannot be the full weight of gravity, as it was
on a horizontal surface. If we make the normal force the Y axis, then the slope of the incline
becomes the X axis. The force of gravity, mg, is still aimed downward toward the center of the
earth.
The normal force pushing the two surfaces together is that component of the mg vector
exerted along the Y axis. The mg vector is the hypotenuse of a right triangle. The component of
mg vector along the Y axis is thus mg times the cosine of theta. This is the normal force pushing
the block against the incline. What is the force of static friction?
The force of static friction is the normal force times the
coefficient of static friction, mu. This is the force
pushing the block up the incline.
What does mg times the sine of theta represent?
The gravitational force trying to push the object down
the incline.
The force pushing the block down the incline, then, is
the difference between mg times the sine of theta,
pushing the block down the incline, and the force of static friction, mg times the cosine of theta
times mu, pushing the block up the incline.
Suppose the incline is 30 degrees, and the coefficient of static friction is 0.3? What is the
acceleration of the block when it begins to slide?
This net force equals the block’s mass times its acceleration down the incline.
We already know that the Net Force also equals: mg
(sin 30 - mu cos 30). So, mass times acceleration down
the incline equals mass times gravity times the sine of
30 degrees minus mu times the cosine of 30 degrees.
The masses cancel out, leaving acceleration equal to
the acceleration of gravity times the sine of 30 degrees
minus mu times the cosine of 30 degrees.
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The block accelerates down the incline at 2.4 meters per seconds squared. Mass is
unimportant. At the moment the downward force of gravity overcomes the force of static
friction, the block, no matter what its weight, will slide down this smooth incline with an
acceleration of 2.4 meters per second squared.
Does the block slide down the incline at a constant
speed or a changing speed?
Since the net force pushing the block down the incline
is continually acting on the sliding box, the box will
accelerate at an ever-increasing speed. Objects move
at a constant speed only when no force is acting on
them.
Slide 20: How can a parked car sit on a hill?
Streets in San Francisco are very steep. How steep can a street be without a parked car sliding
down the street? The static coefficient for rubber on concrete is 0.7.
If a car is not moving, the force pushing the car down
the street must be less than the force of static friction.
As seen in the last problem, the force pushing the car
down an incline is mg times the sine of theta.
The force of static friction is mg times the cosine of
theta times mu.
At the moment the force pushing the car down the
street equals the force of static friction, mg times the
sine of theta equals mg times the cosine of theta times
mu.
The down-slope vector is the mass of the car times the
acceleration of gravity times the sine of theta. The upslope vector is the mass of the car times the acceleration
of gravity times the cosine of theta times the coefficient
of static friction.
When mass times gravity cancels out, the sine of theta
equals the cosine of theta times mu.
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mu equals the sine of theta divided by the cosine of theta. This is the same as saying mu equals
the tangent of theta.
The problem stated that the coefficient of static friction was 0.7, so 0.7 equals the tangent of
theta. If the tangent of theta equals 0.7, theta must be 35.0 degrees. The street cannot be more
than 35.0 degrees steep.
Slide 21: Pulleys and moving masses
Pulleys give us a real chance to analyze force vectors, because two masses are moving
simultaneously. Each mass is being pulled in a different direction, and even though the two
masses are attached to the same cable, the cable may be exerting a different force on each
mass. The good news is that the two masses are attached to each other, so they move at the
same rate.
In this pulley problem, a 2.0 kg block moves across a wooden table, pulled by a 10.0 kg block
with a weightless cable across a frictionless pulley. The coefficient of friction for the block on
the table is 0.5. How fast do the two masses accelerate?
What are the two forces acting on each block? Force is mass times acceleration. The 10.0 kg
block is being pulled downward by the force gravity, which is mass times gravity, and pulled
upward by the cable exerting an upward tension, which we’ll call FT.
The net force is the difference between these two vertical forces. Mg minus FT is 10.0 kg x 9.8
m/sec2 - FT, or 98.0 kg m/sec2 - FT.
The 2.0 kg block is being pulled to the right by the tension in the cable, FT, and pulled to the left
by the force of friction, which is the weight of the block, mg, times the coefficient of static
friction. The net force is FT – mg times mu: FT – 2.0 kg times 9.8 m/sec2 times 0.5.
If these two blocks were on a level plane, you would have no trouble calculating the total force
acting both blocks. You would simply add up the forces acting on each block individually. The
mere fact that the direction of movement for one of the blocks has been redirected downward
should make no difference. You still add up the forces acting on each block to get the total force
acting on both blocks.
The sum of the forces acting on both blocks is 98.0 kgm/s2 – FT for the vertical block, and FT - 9.8
kgm/s2 for the horizontal block. When added together, the two FT’s cancel out and the total
force acting on both blocks is 88.2 kg meters per second2, or 88.2 newtons.
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88.2 newtons is the mass times the acceleration for both blocks moving together, but it doesn’t
tell you the acceleration of the two blocks, and that’s what the problem asked for. How do you
get the acceleration?
Force is mass times acceleration. The force of 88.2 kg
meters per second squared must equal the combined
weight of both blocks, 12.0 kg, times their
acceleration. Their acceleration is, therefore, 7.4
meters per second squared. Each block accelerates 7.4
meters per second squared.
To get the tension on the cable, FT, use the formula
for net downward or horizontal force. For example,
the net downward force, ma, equals the mg minus FT.
Since the acceleration for both blocks is 7.4 m/s2,
(10.0 kg) (7.4 m/s2) = (10.0 kg) (9.8 m/s2) - FT.
74.0 kgm/s2 = 98.0 kgm/s2 - FT
FT = 24.0 kgm/s2, or 24.0 newtons.
Slide 22: Let’s try another method.
Let’s review this pulley problem using capital M for the horizontally-moving mass and small m
for the vertically-moving mass. FT is the tension in the cable, Ff the force of friction, mu the
coefficient of friction, and g gravity.
The force acting on both masses together equals the net
force acting on the vertical block plus the net force
acting on the horizontal block. Since both masses
accelerate equally, the force acting on both blocks
together is their combined mass times their acceleration.
The net force acting on the vertical block is mg minus the
force exerted by the cable, FT. The next force acting on
the horizontal block is the force exerted by the cable
minus the force of static friction, mg times mu.
By algebra, the acceleration is g times the ratio of the little m minus large M times mu over
their combined masses.
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If the mass of little m is 10 kilograms, and large M 2 kilograms, and the coefficient of friction
0.5, then the acceleration is three quarters the acceleration of gravity, a = 7.4 kilogram meters
per second squared, which is the same answer we got before.
Slide 23: Acceleration of an ascending elevator
How fast does this elevator accelerate downward if the elevator and its cargo weigh 1100.0 kg
and the counterweight weighs 1000.0 kg? FT represents
the force of tension exerted by the cable. Assume no
friction when the elevator moves.
As we did before, the force on both masses combined
must equal the sum of the forces on each individual
mass. Capital M will be the mass of the elevator and
small m the mass of the counterweight.
The net force on the elevator is the force of gravity, capital M
times g, minus the upward force exerted by the cable, labeled
FT in the diagram.
The net force on the counterweight is the upward force by the cable, FT, minus the downward force of
gravity, little m times g.
When the force on the elevator and the force on the
counterweight are added together, the negative FT and
positive FT cancel out, and we’re left with the total mass of
the elevator and counterweight times their accleration
equaling the force of gravity on the elevator minus the force
of gravity on the counterweight.
The acceleration of both the elevator and the
counterweight works out to be the acceleration of
gravity times the difference in their masses divided by the sum of the masses.
Plugging in the numbers, we get an acceleration of 0.47 kg meters per second squared, or 1.53
feet per second squared.
How strong does the elevator cable have to be when the elevator ascends?
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Slide 24: Tension on the elevator cable
When the elevator is at rest, the cable must be strong enough to hold the elevator against the
force of gravity: capital M times g.
When the elevator is ascending, however, the cable now
has to be strong enough to lift the elevator against the
force of gravity and also withstand the force of the
counterweight pulling upward on the cable connected to
the elevator. The force exerted by the counterweight is
its weight, little m, times its downward acceleration.
In the last slide, we derived the acceleration for an
elevator and its counterweight, or for the upward and
downward movement of any two masses draped over a pulley. The acceleration of an
ascending elevator is the acceleration of gravity times the difference in the two masses divided
by the sum of the two masses.
With a little algebra, the formula for force on the cable
pulling up the elevator becomes the mass of the elevator
times acceleration of gravity times 1 plus, again, the
difference in the two masses divided by the sum of the
two masses.
What this formula says is that when the elevator is
ascending, the mass of the elevator and its passengers
feels heavier, by an amount equal to their weight, Mg,
times the difference in mass of the elevator and
counterweight, divided by the their sum.
During the ascent of our 1100 kg elevator, everyone feels 5% heavier, including the elevator.
The elevator feels 5% of 1100 kg, or 55 kg heavier, so the cable has to be strong enough to lift
1155 kg.
Slide 25: What you know so far
1. Newton’s first law says that anything not being acted on by a force will continue doing what
it is doing until a force does act on it.
2. Newton’s second law, force equals mass times acceleration, says that when a force does act
on an object, the object will accelerate, meaning change its speed or direction, or both, at a
rate inversely proportional to its mass.
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3. Newton’s third law says that the new force will be met by an equal and opposite force, which
will also obey Newton’s second law. So, if an astronaut pushes on the space station, the space
station pushes back with an equal force, and both forces result in the astronaut and the space
station accelerating away from each other at a rate inversely proportional to their masses. With
less mass, the astronaut accelerates away faster than the space station.
Slide 26: What you know so far
4. Friction is a force whose vector points in the direction opposite to the force trying to move
one object along the surface of another. On a horizontal surface, the magnitude of the force of
friction is the weight of the object being moved times the coefficient of static fraction. When
the surface is not horizontal, the force of friction is that component of the weight of the object
that lies along the line perpendicular to the surface between the two objects, called the
“normal.”
5. Pulley problems involve two masses being subjected to different net forces, but which
experience the same acceleration. The net force on each mass involves analyzing the force
exerted by gravity and the force exerted by the cable attached to the top of each mass. The
force being exerted by gravity may be a frictional force opposing movement of one of the
masses.
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