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Are you accelerating when your speed decreases?
Yes! If you are walking east and you come to a stop, it is because you accelerated to the west! By
"deceleration" we mean acceleration in the direction opposite our direction of motion. Thus in a car,
when you stomp on the brake and decelerate, you are actually accelerating toward the rear of the car
(in the direction opposite its direction of motion).
As the Space Shuttle falls, does it accelerate forever and does it go faster and faster?
Yes to the first part, no to the second part. Remember that acceleration can change the direction of
velocity without changing the magnitude of velocity (the speed of the object). When the space shuttle
accelerates, its speed doesn't change, only its direction of travel. Although it accelerates endlessly, it
never goes faster or slower. Actually, if the shuttle's orbit isn't circular, its speed does increase and
decrease slightly as it orbits the earth in an ellipse, but that's an unimportant detail. For a circular
orbit, the shuttle's speed is constant but its velocity (speed and direction) is not constant!
Does a bullet go from 0 to maximum speed instantly?
The bullet accelerates gradually, like everything else. However, the forces that push on the bullet
when the gun is fired are extremely large and it accelerates extremely rapidly. It goes from 0 to
maximum speed in about a thousandth of a second.
Does air resistance affect a horizontally thrown ball?
Yes. A ball thrown horizontally gradually loses its downfield component of velocity. For that reason,
you must throw a ball somewhat below the 45° angle from horizontal in order to make it travel as far
as possible. Actually, the air has even more complicated effects on spinning balls.
Doesn't weight have resistance to acceleration?
No, weight measures a different characteristic of an object. Mass measures inertia (or equivalently
resistance to acceleration). But weight is just the force that gravity exerts on an object. While an
object that has great weight also has great mass and is therefore hard to accelerate, it's not the weight
that's the problem. To illustrate this, imagine taking a golf ball to the surface of a neutron star, where
it would weigh millions of pounds because of the incredibly intense gravity. That golf ball would still
accelerate easily because its mass would be unchanged. Only its weight would be affected by the local
gravity. Similarly, taking that golf ball to deep space would reduce its weight almost to zero, yet its
mass would remain the same as always.
How can an object in space "fall"?
Gravity still acts on objects, even though they are in space. No matter how far you get from the earth,
it still pulls on you, albeit less strongly than it does when you are nearby. Thus if you were to take a
ball billions of miles from the earth and let go, it would slowly but surely accelerate toward the earth
(assuming that there were no other celestial objects around to attract the ball—which isn't actually the
case). As long is nothing else deflected it en route, the ball would eventually crash into the earth's
surface. Even objects that are "in orbit" are falling; they just keep missing one another because they
have large sideways velocities. For example, the moon is orbiting the earth because, although it is
perpetually falling toward the earth, it is moving sideways so fast that it keeps missing.
I can accept that weight is a force, but it doesn't seem to follow common sense to me.
It would seem like a force if you had to lift yourself up ladder. Imagine carrying a friend up the
ladder; you'd have to pull up on your friend the whole way. That's because some other force (your
friend's weight) is pulling down on your friend. But when you think of weight as a measure of how
much of you there is, then it doesn't seem like a force. That's where the relationship between mass and
weight comes into play. Mass really is a measure of how much of you there is and, because mass and
weight are proportional to one another, measuring weight is equivalent to measuring mass.
I don't understand the horizontal component of a ball thrown downfield. Does it have constant
velocity and/or acceleration, even at the start?
Until you let go of the ball, you are in control of its velocity and acceleration. During that time, it does
accelerate and its velocity isn't constant. But as soon as you let go of the ball, everything changes. The
ball's motion in flight can be broken up into two parts: its vertical motion and its horizontal motion.
Horizontally, the ball travels at a constant speed because there is nothing pushing or pulling on it
horizontally (neglecting air resistance). Vertically, the ball accelerates downward at a constant rate
because gravity is pulling down on it. Thus the ball travels steadily forward in the horizontal direction
as it fall in the vertical direction. Of course, falling can begin with upward motion, which gradually
diminishes and is replaced by downward motion.
I don't understand the relationship between mass, acceleration, and force in Newton's second
law.
First off, force causes acceleration. The stronger that force, the more the acceleration. In fact, the two
are exactly proportional to one another: double the force and you double the acceleration. Secondly,
mass resists acceleration. The more mass an object has, the less it accelerates. The two are exactly
inversely proportional to one another: double the mass and you halve the acceleration. These two ideas
can be combined into one observation: the force you exert on an object is equal to the product of its
mass times the acceleration it experiences. Look at that relationship: if you double the force you exert
on an object, you double its acceleration, so that part checks out. If you double the object's mass and
leave the force unchanged, then the acceleration must be halved, so that part checks out. Thus
Newton's second law is simply a sensible relationship between the force you exert on an object, its
mass, and its acceleration.
If a projectile released or hit at a 45° angle above horizontal should go the farthest, then why, in
the game of golf, does the three iron (20° loft) hit a golf ball so much farther in the air than, say,
a seven iron (approximately 45° loft) if the same technique and force are produced by the
golfer? Is it backspin, shaft length, etc.?
It's backspin! Air pushes the spinning ball upward and it flies downfield in much the same way as a
glider. When you throw a glider for distance, you concentrate your efforts on making it move
horizontally because the air will help to keep the glider from hitting the ground too soon. Similarly,
the air holds the spinning golf ball up for a remarkably long time so that giving the ball lots of
downfield speed is most important for its distance. That's why a low-loft club like a three iron sends
the ball so far.
If force causes only acceleration and not velocity, does a machine (i.e. an engine) that causes a
constant velocity in an adjacent object not exert a force?
If that adjacent object is free of any other forces, then no, the machine does not exert a force on it!
This is a wonderful question, because it points toward many of the issues concerning energy and work.
The bottom line is this: if some object is truly free moving (no other forces on it), it will move along
at constant velocity without anything having to push on it. For example, if your car were truly free
moving (no friction or air resistance), then it would coast forever on a level surface and the engine
wouldn't have to do anything. You could even put the car in neutral and turn off the engine. The only
reason that you need an engine to keep pushing the car forward is because friction and air resistance
push the car backwards.
If the Space Shuttle is always falls toward the center of the earth, how does it get to outer space?
If something accelerates, doesn't it go faster and thus have its speed increase?
The second question first: no, an object can accelerate without going faster. In fact, a stopping object
is accelerating! If an accelerating object can speed up or slow down, it can certainly maintain a
constant speed. If you swing a ball around in a circle on a string, that ball is accelerating all the time
but its speed isn't changing.
Now the first question: for the space shuttle to reach orbit, it needs an additional force in the upward
direction. It obtains that force by pushing exhaust gas downward so that the exhaust gas pushes it
upward. During the time when it's heading toward orbit, it's not falling because it has an extra upward
force on it. However, the Space Shuttle can leave its orbit and head off into outer space by traveling
faster than it normally does. It acquires this increased speed by firing its rocket engines again. Its
usual speed keeps it traveling in a circle near the earth's surface. If it went a bit faster, its path
wouldn't be bent downward as much and it would travel more in a straight line and away from the
earth. It would still be falling toward the earth (meaning that it would still be accelerating toward the
earth), but its inertia would carry it farther away from the earth. If the Shuttle had enough speed, it
would travel to the depths of space before the earth had time to slow its escape and bring it back.
If you drop a penny from the Empire state building - could it really puncture a hole in a car
because of its constant acceleration?
Probably not. If the penny were to fall sideways, so that it had as little air resistance as possible, it
would reach about 280 km/h (175 mph). That speed ought to be enough to drive the penny into the car
if its top were thin enough. However, studies have shown (see ) that coins tumble as they fall and
experience substantial air resistance. As a result, you could probably catch a falling penny in your
hand, although it might sting a bit. A falling ballpoint pen, because of its aerodynamic shape, is
another matter.
If you dropped a bullet and at the same time, fired a bullet directly at the ground, wouldn't the
bullet fired at the ground hit the ground first?
Sure it would. The fired bullet will only hit the ground at the same time as the dropped bullet if the
fired bullet is shot exactly horizontally. If you fire the bullet at the ground, then it starts out with an
enormous downward component to its velocity. The falling bullet doesn't have this initial downward
component to its velocity and never catches up.
If you fire a bullet horizontally and drop an identical bull at the same moment, will they both
hit the ground at the same time?
Yes. The fired bullet may travel farther, but it will fall just as quickly as the dropped bullet and they'll
hit the ground at the same moment. This effect explains why you must aim above the target when
shooting at something far away. The faster the bullet travels to the target, the less it will drop. An
arrow travels slowly enough that it will fall a considerable distance en route. You must aim quite high
when shooting an arrow.
If you had an object in an empty sphere with a radius of a few miles, surrounded by equally
distributed and very concentrated mass, what effects of gravity would the object feel?
As long as the mass isn't so concentrated that the laws of general relativity become important, the
object won't feel any gravity at all. The forces from opposite sides of the surrounding mass will cancel
exactly. For example, if you were at the center of the earth in a large spherical opening, you would be
perfectly weightless. The force from the north side of the earth would balance the force from the south
side. This effect is quite remarkable and depends on the fact that gravity becomes weaker as the
inverse square of the distance separating two objects. That way, even if you aren't in the exact center
of the earth, the forces still cancel.
If you jump off of a diving board, are you exerting force on the board or is it exerting force on
you?
Actually, as you stand on the end of the board or as you push off from its end, you are pushing on the
board and it is pushing back on you. The forces you exert on one another are exactly equal in amount
but opposite in direction. That observation is called Newton's third law of motion and is the real
meaning behind the phrase "for every action there is a reaction."
If you shot a gun and dropped a bullet at the same time, how could they land at the same time?
Wouldn't the acceleration behind the bullet keep it in the air longer?
If you shot the bullet horizontally, it really would hit the ground at the same time as the bullet you
simply dropped. During the firing, the bullet would accelerate like crazy, but only horizontally. It
would leave the gun with a velocity that was only in the horizontal direction. With no forces pushing
on it horizontally after that (we'll neglect air resistance), the bullet will make steady progress
downfield. But at the same time, it will begin to fall. The vertical component of its velocity will
gradually increase in the downward direction as it falls. Like the dropped bullet, it will drift downward
faster and faster and the two will hit the ground together.
In what sense is the Space Shuttle falling toward the earth?
When the space shuttle circles the earth, it's experiencing only one force: the force of gravity. As a
result, it's perpetually accelerating toward the earth's center. If it weren't moving initially, it would
begin to descend faster and faster until...splat. But it is moving sideways initially at an enormous
speed. While it accelerates downward, that acceleration merely deflects its sideways velocity slightly
downward. Instead of heading off into space, it heads a little downward. But it never hits the earth's
surface. Instead, it arcs past the horizon and keeps accelerating toward the center of the earth. In short,
it orbits the earth—constantly accelerating toward the earth but never getting there.
Is it possible for a ball to fall to earth at a different angle from the one at which it rose?
If the ground is level and there were no air resistance, the answer would be no. The flight of the ball is
perfectly symmetric. It rises to a maximum height in a parabolic arc and then returns to the ground as
the continuation of that same parabolic arc.
However, if the ground isn't level, then the angle it hits the ground at might be different. For example,
if you toss a ball almost horizontally off a cliff, it will hit the ground almost vertically. Horizontal and
vertical are two very different directions.
Air resistance also tends to slow a ball's motion and it's particularly effective at stopping the
downfield component of its velocity. Gravity makes sure that the ball descends quickly, but there is no
force to keep the ball moving downfield against air resistance. The result is that balls tend to drop
more sharply toward the ground. When you hit a baseball into the outfield, it may leave your bat at a
shallow angle but it will drop pretty vertically toward the person catching it.
Finally, if the ball is spinning, it can obtain special forces from the air called lift forces. These forces
can deflect its path in complicated ways and are responsible for curve balls in baseball, slices and
hooks in golf, and topspin effects in tennis.
Is it possible for a skydiver who jumps second from a plane to put himself in an aerodynamic
position and overtake a person who jumped first?
Yes. When you skydive, your velocity doesn't increase indefinitely because the upward force of air
resistance eventually balances the downward force of gravity. At that point, you reach a constant
velocity (called "terminal velocity"). Just how large this terminal velocity is depends on your shape. It
is possible to increase your terminal velocity by rolling yourself into a very compact form. In that
case, you can overtake a person below you who is in a less compact form.
Is there a fixed amount of force in the universe?
No, forces generally depend on the distances between objects, so that two objects that are moving
together or apart will experience different amounts of force as they move about. As a result, the total
amount of force anywhere can change freely. But there are quantities that have fixed totals for the
universe. The most important of these so-called "conserved" quantities is energy.
Isn't there "some" acceleration at the very start and very end of an elevator ride? Why does
one's stomach take a flop when the elevator stops and not when it starts?
Yes, there is acceleration at the start and stop of an elevator ride. As the car starts, it accelerates
toward the destination and as the car starts, it accelerates in the opposite direction. Your stomach
takes a flop whenever you feel particularly light, as when you are falling or otherwise accelerating
downward. As you accelerate downward, your body doesn't have to support your stomach as much as
normal and you feel strange. In fact, you feel somewhat weightless. You have this feeling whenever
the elevator starts to move downward (and therefore accelerates downward) or stops moving upward
(and there accelerates downward).
What is the difference between mass and weight?
Mass is the measure of an object's inertia. You have more mass than a book, meaning that you are
harder to accelerate than a book. If you and the book were each inside boxes, mounted on wheels, I
could quickly determine which box you were in. I would simply push on both boxes and see which one
accelerated most easily. That box would contain the book and you would be in the box that's hard to
accelerate. Weight, on the other hand, is the amount of force that gravity (usually the earth's gravity)
exerts on an object. You weigh more than a book, meaning that the earth pulls downward on you
harder than it does on the book. Again, I could figure out which box you were in by weighing the two
boxes. You'd be in the heavier box. So mass and weight refer to very different characteristics of
objects. They don't even have the same units (mass is measured in kilograms, while weight is
measured in newtons. But fortunately, there is a wonderful relationship between mass and weight: an
object's weight is exactly proportional to its mass. Because of this relationship, all objects fall at the
same rate. Also, you can use a measurement of weight to determine an object's mass. That's what you
do when you weigh yourself on a bathroom spring scale; you are trying to determine how much of you
there is-your mass-but you are doing it by measuring how hard gravity is pulling on you—your
weight.
When you pushed the baseball and bowling ball with an equal force, the baseball went farther
on the table because it has a smaller mass. If gravity also exerts an equal force on the 2 balls,
like your push, then why do they fall at equal speeds?
The answer is that gravity doesn't exert equal forces on the 2 balls! It pulls down harder on the
bowling ball than it does on the baseball. Suppose the bowling ball has 10 times the mass of the
baseball. Then gravity will also exert 10 times the force on the bowling ball that it exerts on the
baseball. The result is that the bowling ball is able to keep up with the baseball! The bowling ball may
resist acceleration more than the baseball, but the increased gravitational force the bowling ball
experience exactly compensates.
When you shoot a bullet straight upward, doesn't it accelerate upward?
When you shoot a bullet upward, is does accelerate as long as it's in the gun. The burning gases push
upward on the bullet and it accelerates upward. But as soon as it leaves the gun, it's a falling object,
with the only force on it being gravity (and air resistance).
When you throw a ball upward, what force pushes it upward?
To throw the ball upward, you temporarily push upward on it with a force greater than its weight. The
result is that the ball has a net force (the sum of all forces on the ball) that is upward. The ball
responds to this upward net force by accelerating upward. You continue to push upward on the ball for
a while and then it leaves your hand. By that time, it's traveling upward with a considerable velocity.
But once it leaves your hand, it is in free fall. Nothing but gravity is pushing on it—it's carried upward
by its own inertia! In fact, it's accelerating downward at 9.8 m/s^2. It rises for a while, but less and
less quickly. Eventually it comes to a stop and then it begins to descend.
While gravity supposedly makes all objects accelerate at the same rate, feathers do not seem to
comply. What factors affect the feather's acceleration, besides air resistance (which should
affect all objects equally)?
Actually, air resistance doesn't affect all objects equally. The feather has so much surface area that it
pushes strongly on the air through which it moves and the air pushes back. For an object with very
little mass and weight, the feather experiences an enormous amount of air resistance and has great
difficulty moving through the air. That's why it falls so slowly. If you were to pack a feather into a
tiny pellet, it would then fall just about as fast as other objects. Similarly, you fall much more slowly
when your parachute is opened because it then interacts with the air much more effectively.
Why do objects on earth accelerate downward at the same speed regardless of their mass?
What you mean here is that they accelerate downward at the same rate ("speed" has a particular
meaning that isn't so well suited to discussions of acceleration). This fact comes about because,
although massive objects are harder to accelerate, they also experience more weight. Thus a huge
stone will fall at the same rate as a small rock because the stone will be pulled downward more
strongly by gravity and that extra pull will make up for the stone's greater inertia.
Why do two objects of unequal mass fall and hit the ground at the same time?
If one object has twice the mass of the other, then it is twice as hard to accelerate. To make it keep
pace with the other ball, it must experience twice the force. Fortunately, gravity pulls on it twice as
hard (it has twice the weight of the other ball), so in falling, it does keep pace with the other ball. The
two fall together. Just for fun, imagine stepping off the high diving board with two friends. The three
of you have essentially identical masses and weights and also fall at the same rate. Now imagine that
two of you hold hands as you fall. You are now a single object with twice the mass of your other
friend. Nonetheless, you still fall at the same rate. So an object with twice the mass of another falls at
the same rate as that other object.
Why do you feel no acceleration in free fall, even though you are accelerating?
This wonderful question has many answers. The first, and most direct, is that you do feel the
acceleration. You feel an upward fictitious force (not a real force at all, but an effect of inertia) that
exactly balances your downward weight. The feeling you experiences is "weightlessness." That's why
your stomach feels so funny. You're used to having it pulled downward by gravity but the effect of
your fall is to make it feel weightless.
Why does a ball fall 4.9 meters during its first second of falling?
As a simple argument for that result, think about the ball's speed as it falls: it starts from rest and,
over the course of 1 second, it acquires a downward speed of 9.8 m/s. Its average speed during that
first second is half of 9.8 m/s or 4.9 m/s. And that is just how far the ball falls in that first second: 4.9
m. By holding the ball 4.9 m above the floor, you can arranged for it to hit one second after you drop
it.
Why does an object accelerate when it changes direction?
What you mean by "changes direction" is that the direction part of its velocity changes. For example,
instead of heading east at 10 m/s (or 10 miles-per-hour, if that feels more comfortable), it heads north
at 10 m/s (or 10 miles-per-hour). This change in direction involves acceleration. The car must
accelerate toward the west in order to stop heading east, and it must accelerate toward the north in
order to begin moving north. Actually, it probably does both at once, accelerating toward the
northwest and shifting its direction of motion from eastward to northward.
Why is 45° above horizontal the ideal angle to throw something the greatest distance if gravity is
acting on the vertical direction but not the horizontal?
The 45° angle is ideal because it gives the ball a reasonable upward component of velocity and also a
reasonable downfield component of velocity. The upward component is important because it
determines how long the ball will stay off the ground. The downfield component is important because
it determines how quickly the ball will travel downfield. If you use too much of the ball's velocity to
send it upward, it will stay off the ground a long time but will travel downfield too slowly to take
advantage of that time. If you use too much of the ball's velocity to send it downfield, it will cover the
horizontal distances quickly but will stay of the ground for too short a time to travel very far. Thus an
equal balance between the two (achieved at 45°) leads to the best distance. Note that this discussion is
only true in the absence of air resistance.
Why is force = mass * acceleration an exact relationship (i.e. why not force = 2 * mass *
acceleration)?
The answer to this puzzle lies in the definition of force. How would you measure the amount of a
force? Well, you would push on something with a known mass and see how much it accelerates! Thus
this relationship (Newton's second law) actually establishes the scale for measuring forces. If your
second relationship were chosen as the standard, then all the forces in the universe would simply be
redefined up by a factor of two! This redefinition wouldn't harm anything but then Newton's second
law would have a clunky numerical constant in it. Naturally, the 2 is omitted in the official law.
Why on Pg. 6, 2nd full paragraph, it says the car is accelerating if the slope of the road changes
but in the "not accelerating" list it says a bicycle going up a hill is not accelerating. Aren't those
the same situation?
Here is why the two situations are different:
In the first case, the car is traveling on a road with a changing slope. Because the road's slope
changes, the car's direction of travel must change. Since velocity includes direction of travel, the car's
velocity must change. In short, the car must accelerate. Picture a hill that gradually becomes steeper
and steeper—the car's velocity changes from almost horizontal to almost vertical as the slope changes.
In the second case, the bicycle is climbing a smooth, straight hill at a steady speed. Since the hill is
smooth and straight, its slope is not changing. Since the bicycle experiences no change in its direction
of travel or its speed, it is traveling at a constant velocity and is not accelerating.
How do you push a shopping cart and have the cart exert the same force on you, if you are still
traveling forward? Friction? Air Resistance?
When you push a shopping cart straight forward down an aisle, you are pushing it forward and it is
pushing you backward. If nothing else were pushing on the two of you, the cart would accelerate
forward and you would accelerate backward. But the cart is experiencing friction and air resistance,
both of which tend to slow it down. They are pushing the cart backward (in the direction opposite its
motion). So you must keep pushing it forward to ensure that it experiences zero net force and
continues at constant forward velocity. As for you, you need a force to keep yourself heading forward;
otherwise the cart's backward force on you would slow you down. So you push backward on the
ground with the soles of your shoes. In return, the ground pushes on you (using friction) and propels
you forward. As a result, you also experience zero net force and move forward at constant velocity.
How does a surface know how hard it must push upward on an object to support that object?
If you put a piano on the sidewalk, the piano will settle into the sidewalk, squeezing the sidewalk's
surface until the sidewalk stops it from descending. At that point, the sidewalk will be pushing upward
on the piano with a force exactly equal in magnitude to the piano's downward weight. The piano will
experience zero net force and will not accelerate. It's stationary and will remain that way.
But if the sidewalk were to exert a little more force on the piano, perhaps because an animal under the
sidewalk was pushing the sidewalk upward, the piano would no longer be experiencing zero net force.
It would now experience an upward net force and would accelerate upward. The piano would soon rise
above the sidewalk. Of course, once it lost contact with the sidewalk, it would begin to fall and would
quickly return to the sidewalk.
For an example of this whole effect, put a coin on a book. Hold the book in your hand. The book is
now supporting the coin with an upward force exactly equal to the coin's weight. Now hit the book
from beneath so that it pushes upward extra hard on the coin. The coin will accelerate upward and leap
into the air. As soon as it loses contact with the book, it will begin to fall back down.
Thus, if the sidewalk pushed upward too hard, the piano would rise upward and leave the sidewalk's
surface and if the sidewalk pushed upward too weakly, the piano would sink downward and enter the
sidewalk's surface. A balance is quickly reached where the sidewalk pushes upward just enough to
keep the piano from accelerate either up or down.
If a falling egg weighs only 1 newton, how can it exert a force of 1000 newtons on a table when it
hits?
As the egg falls, it is experiencing only one force: a downward weight of 1 N. But when it hits the
table, it suddenly experiences a second force: an upward support force of perhaps 1000 N. The table is
acting to prevent the egg from penetrating its surface. The net force on the egg is then 999 N, because
the upward 1 N force partially cancels the downward 1000 N force. If the egg could tolerate such
forces, it would accelerate upward rapidly and wouldn't enter the table's surface. Because the egg is
fragile, it shatters. The force that the egg exerts on the table is also 1000 N, this time in the downward
direction. The egg and table push on one another equally hard. The table doesn't move much in
response to this large downward force because it's so massive and because it's resting on the floor. But
if you were to put your hand under the falling egg, you would feel the egg push hard against your hand
as it hit.
If every force always has an equal and opposite force pushing against it (like the bowling ball
and your arm in today's lecture), how can anything at all accelerate? Wouldn't forces always
cancel each other out?
The two equal but opposite forces are being exerted on different objects! In many cases, those two
objects are free to accelerate independently and they will accelerate—in opposite directions! For
example, when I push on a bowling ball, it pushes back on me with an equal but opposite force. If my
force on the bowling ball is the only force it experiences, it will accelerate in the direction of my force
on it. Since it exerts an opposite force on me, I will accelerate in the opposite direction—we will push
apart!
If it takes less force to push something up a ramp, why doesn't it also take less work?
When you lift an object using a ramp, the uphill force you exert on it is less than its weight but the
distance you must travel along the ramp is more than if you simply lifted the object straight up. Since
the work you do on the object is the product of the force you exert on it times the distance it travels in
the direction of that force, the work isn't changed by using the ramp. For example, if you lift a cart
weighing 15 N straight up for 0.2 meters, you do 3 newton-meter or 3 joules of work on it. To raise
that cart that same 0.2 meters upward on the ramp, you'd have to exert a 3 N force on it as you pushed
it 1.0 meter along the ramp. The work you'd do to raise the cart by pushing it up the ramp would be 3
joules again. No matter how you raise the cart to the height of 0.2 meters, you're going to do 3 joules
of work on it.
If Newton's third law is true - then how can you move anything? If it exerts the exact same
amount of force on you that you exert on it, wouldn't the net force be zero and the object
wouldn't move?
The total force on the two of you (the object you're pushing on and you yourself) would be zero, but
the object would be experiencing a force and you would be experiencing a force. As a result, the object
accelerates in one direction and you accelerate in the other! To see this, imaging standing on a frozen
pond with a friend. If the two of you push on one another, you will both experience forces. You will
push your friend away from you and your friend will push you in the opposite direction. You will both
accelerate and begin to drift apart. Each of you individually will experience a net force. (It's true that
the two of you together will experience zero net force, which means that as a combined object, you
won't accelerate. The way this appears is that your overall center of mass won't accelerate. It will
remain in the middle of the pond even as the two of you travel apart toward opposite sides of the
pond.)
If the downward motion of lifting a weight transfers energy to you, why does your arm get
tired?
Your body is unable to store working that's done on it and also wastes energy even when it is not doing
any work. When you lower a weight, the weight does transfer energy to you, but your body turns that
energy into thermal energy. You get a little bit hotter. If you were made out of rubber, you might store
it as elastic potential energy (like a stretched rubber band). Instead, your muscles don't save the
energy in a useful form. As for getting tired, your muscles turn food energy into thermal energy even
when you aren't doing work. That's what happens during isometric exercises. There's nothing you can
do about it. It's like a car, which wastes energy when it's stopped at a light.
Is it impossible to do work on a ball while carrying it horizontally, or were you only referring to
the force of gravity in the demonstration? Or must you be "pushing" the ball?
When I carried the ball horizontally at constant velocity, I did no work on the ball. That's because the
force I exerted on the ball was directly upward and the direction the ball moved was exactly
horizontal. Since work is force times distance in the direction of that force, the work I did was exactly
zero. But when I first started the ball moving horizontally, there was a brief period during which I had
to push the ball forward horizontally. That's when I "got the ball moving." During that brief period, I
did do work on the ball and I gave it kinetic energy. It needed that kinetic energy to move
horizontally. When I reached my destination, there was a brief period during which I had to pull the
ball backward horizontally. That's when I "stopped the ball from moving." During that brief period, I
did negative work on the ball and removed its kinetic energy.
What forces are involved when a football player who is running is tackled by another player?
If the two players collide hard, they will both exert enormous forces on one another. The player
running toward the right will experience a force to the left and will accelerate toward the left (slowing
down). The player running toward the left will experience a force to the right and will accelerate
toward the right (slowing down). The forces involved would cause bruises if they weren't wearing
pads. The pads reduce the magnitudes of the forces on their skin by prolonging the accelerations
(smaller forces exerted for longer times). If one player simply trips up the other player, then the
player who falls will still come to a stop. However, that player will be experiencing most of the
stopping force from the ground by way of sliding friction.
What happens with things like liquids "falling" onto objects like sponges? Does the sponge exert
an upward force onto the liquid?
When liquids fall onto sponges, the sponges do exert upward forces on the liquids. Otherwise, the
liquids would continue to fall. When a raindrop hits your hair, you can feel it push on your hair and
your hair pushes back, stopping the raindrop's descent.
When a falling egg hits a table and breaks, did it fail to push equally on the table?
No. It pushed hard against the table and the table pushed hard against it. The forces exerted were
exactly equal but in exactly the opposite directions. Each object experienced a strong push from the
other object. But as they say, "whether the rock hits the pitcher or the pitcher hits the rock, it's bound
to bad for the pitcher." The egg couldn't take the push and it broke.
When a person bumps into something or has something dropped on them and a bruise forms,
does it form because of the object hitting the person or from the person exerting a force on the
object to keep that object from pass through their skin?
The bruise forms because of the force exerted on the person by the object. When an object hits you,
it's obvious that the object pushes on you. But the object also pushes on you when you hit it. In fact,
it's a matter of perspective which is hitting which. To a person standing next to you when you're hit by
a ball, the ball hit you. To a person running along with the ball, you hit the ball. In each case, the ball
pushes on you and gives you a bruise. You also push on the ball, causing it to accelerate away from
you.
When you drop a glass on a hard floor, why does it sometimes break and sometimes not?
When the glass hits the floor, the floor exerts all of its force on the part of the glass that actually
touches the floor. That small part of the glass accelerates upward quickly and comes to rest. The
remainder of the glass isn't supported by the floor and continues downward. However the glass is
relatively rigid and parts of it begin to exert forces on one another in order to stop the whole glass
from bending. These internal forces can be enormous and they can rip the glass apart. Glass is a
remarkable material; it never dents, it only breaks. As the glass tries to come to a stop, the internal
forces may bend it significantly. It will either tolerate those bends and later return to its original shape
or it will tear into pieces. Which of the two will occur depends critically on the precise locations and
amounts of the forces. If the forces act on a defect on the glass's surface, it will crack and tear and the
glass is history. If the forces all act on strong parts of the glass, it may survive without damage.
When you push up on an object, are you creating thermal energy or does that only occur when
something does work on you?
When you lift a heavy object, you do work on that object. After all, you exert an upward force on it
and it moves in the direction of that force. However your muscles are inefficient and you consume
more food energy (calories) during the lifting process than you actually transfer to the heavy object.
Whatever energy you consume that doesn't go into the object remains in you as thermal energy. Any
time you tighten your muscles, whether you do work on something, it does work on you, or neither
does work on the other, you end up wasting some food energy as thermal energy.
Why doesn't an egg break when it falls into a pile of feathers? Isn't the pile of feathers exerting
the same force on it (perhaps 1000 newtons) that a table would if it were to hit that table?
The egg doesn't break because the feathers exert a much smaller force on the egg than the table would.
The feathers can move so when the egg first hits them, the feathers don't have to stop the egg so
quickly. To keep the egg from penetrating into the table, the table has to stop the egg's descent in
about a thousandth of a second. That required a huge upward force on the egg of perhaps 1000 N. This
large upward force, exerted on one small point of the egg, breaks the egg. But when the egg hits the
feathers, the feathers can stop the egg's descent leisurely in about a tenth of a second. They only have
to push upward on the egg with a smaller force of perhaps 10 N. This modest force, exerted on many
points of the egg, shouldn't break the egg. During this tenth of a second, the feathers and the egg will
both move downward and the egg will come to a stop well below the place at which it first touched the
feathers.
Can you give me an example of when the angular acceleration is in a different direction from
the torque applied?
When an object isn't symmetric, it can rotate in very peculiar ways. If you throw a tennis racket into
the air so that it is spinning about an axis that isn't along the handle or at right angles to the handle, it
will wobble in flight. Its axis of rotation will actually change with time as it wobbles. If you were to
exert a torque on this wobbling tennis racket, its angular acceleration wouldn't necessarily be along
the direction of the torque.
Given a lever long enough, could you move the world?
Yes. Of course, you would need a fixed pivot about which to work and that might be hard to find. But
you could do work on the world with your lever. If the arm you were dealing with was long enough,
you could do that work with a small force exerted over a very, very long distance. The lever would
then do this work on the world with a very, very large force exerted over a small distance.
How can cats turn their bodies around to land on their feet if they fall and how can people do
tricks in the air when they are skydiving if you're supposed to "keep doing what you've been
doing" when you leave the ground?
Cats manage to twist themselves around by exerting torques within their own bodies. They aren't rigid,
so that one half of the cat can exert a torque on the other half and vice versa. Even though the overall
cat doesn't change its rotation, parts of the cat change their individual rotations and the cat manages to
reorient itself. It goes from not rotating but upside down to not rotating but right side up. Overall, it
never had any angular velocity. As for skydiving, that is mostly a matter of torques from the air. As
you fall, the air pushes on you and can exert torques on you about your center of mass. The result is
rotation.
Is moment of inertia determined only by mass, as inertia is in translational motion?
No, moment of inertia embodies both mass and its distribution about the axis of rotation. The more of
the mass that is located far from the axis of rotation, the larger the moment of inertia. For example, a
ball of dough is much easier to spin than a disk-shaped pizza, because the latter has its mass far from
the axis of rotation.
Shouldn't the seesaw be completely horizontal in order to be balanced? How can it be balanced
if it's not horizontal?
A balanced seesaw is simply one that isn't experiencing any torque—the net torque on it is zero.
Because there is no torque on it, it isn't undergoing any angular acceleration and its angular velocity is
constant. If it happens to be horizontal and motionless, then it will stay that way. But it could also be
tilted or even rotating at a steady rate.
What exactly are angular speed and angular velocity?
Angular speed is the measure of how quickly an object is turning. For example, an object that is
spinning once each second has an angular speed of "1 rotation-per-second," or equivalently "360
degrees-per-second." Angular velocity is a combination of angular speed and the direction of the
rotation. For example, a clock lying on its back and facing upward has a minute hand with an angular
velocity of "1 rotation-per-hour in the downward direction." The downward direction reflects the fact
that the minute hand pivots about a vertical axis and that your right hand thumb would point
downward if you were to curl your fingers in the direction of the minute hand's rotation.
What is the difference between right and left hand rules?
The rule that's used in the mechanics of rotation is always the right hand rule and that's important. It
represents a choice made long ago about how to describe an object's rotation. Having made that
choice, it says that the minute hand of a clock (which naturally rotates clockwise) points into the
clock. You know that because if you curl the fingers of your right hand in the direction that the minute