Newton's first law is the most fundamenatal law of motion, but a law which does not always follow our common sense view of physics. You could paraphrase it as the LAW OF INERTIA. It tells you what COULD HAPPEN to an object when NO FORCE acts on the object.

To try and understand easily we could break the law into two parts. The first part of it is obvious.

(i) If no resultant or unbalanced force acts on an object, an object at REST would continue to remain at rest.

The second part does not follow our common sense view of the world. Our ancients did not recognize the importance of this. It reads as follows:

(ii) If no resultant or unbalanced force acts on an object, an object MOVING in a straight line at constant speed (constant velocity) would continue to move along the same straight line at the SAME speed.

Now this is not common sense. When you push something it stops after a while because of the frictional forces which come into play. However in the laboratory we can verify this law using an air track in which a glider moves, somewhat like a hovercraft riding on a cushion of air, with negligible friction. You don't need these gizmos in space because there is practically no friction and the first law is easily verified.

Earlier I had paraphrased it using the word INERTIA. If you're wondering what it is, it is simply the TENDENCY of an object to RESIST any change in its state of motion. You would possibly understand this well in light of what happens when you're either sitting at home watching TV or sleeping. You would like to continue doing that against your families wishes. Alternately you may want to continue playing if you were already playing and not want to return home when your mum calls for you. Think about it!

Force as you may be aware is a vector because the effect of a force depends on BOTH the magnitude and the direction.

The magnitude of a force refers to the AMOUNT or SIZE of the force. It can be defined using Newton's second law as a word equation.

The magnitude of a force can be calculated from the product of the mass and acceleration of an object.

That is, the unbalanced or resultant or net force on an object is the product of the object's mass and the object's acceleration. Mathematically,

F_net = m x a

or

Net Force = mass x acceleration

This is a very basic problem in mechanics involving Newton's second law. According to Newton's second law

Net Force = mass x acceleration

   = 2 x 4
   = 8 N

Physics like other sciences has its own jargon or lingo that we have to first understand. Let's now try and understand the language used here. To put it simply we can say an object is moving if there is a CHANGE in its POSITION with respect to some other object. Here's where we have to be careful. Our intuition is SOMETIMES correct. One has to be careful with intuitive physics.

Now answer this question for me even as you read this answer at home (or work?). What is your speed?

Your answer would have normally been "0" because you were not moving. What you've compared is your position with respect to other positions next to you and found that you're position with reference to them is the same. You're at REST RELATIVE to the stationary objects around you and the ground (Earth). However you very well know that you and I are actually not stationary and are moving at a high speed around the sun. The only advantage is because we are moving WITH the Earth, we do not realize that we are moving. I guess one might be forced to believe this if you're sitting outdoors in the evening and the light disappearing under your very eyes!

Motion as we use in physics is a relative term. You're not in motion with respect to the moving bus. That's what YOU feel. However your position is changing with respect to the surroundings and therefore we say you are moving with reference to the surroundings (and the Earth). Are you following all this?

You're not using any force but you automatically acquire the state of motion of the object you're in, the bus in this case or the Earth if you thought you were at rest. This follows from Newton's first law as well which is sometimes referred to as the law of intertia. Examiners of physics are fond of asking questions on Newton's first law and you can look at my other answers where I've discussed Newton's first law and also worked out numerous problems as well using this subtle concept of CONSTANT VELOCITY.

Energy is a completey different concept but closely related to the concept of WORK.

You need to understand that physicists are particular about the meaning of words they use. In fact, not just physics but in all of science and technology, you have to learn the lingo first. You are confusing the meaning of the words speed and power. They mean totally different things in physics.

Coming to your question, the problem is not as easy as it appears. The first concept you must understand is the forces that are involved here. Two forces dominate in a case such as this, a problem physicist would call "free fall".

The two forces to be considered here are the weight of the object acting downward and the air resistance acting upward.

The weight of the object does not change significantly with distance but can become less if taken to great heights.

The air resistance however is a force which increases as the speed of the object increases, of course until it equals the weight of the object. After that, when the two forces cancel, the object (penny in your case) will continue to fall at a constant speed. This constant speed is called terminal velocity.

I would strongly recommend you read some of my other answers on free fall and Newton's first law. Getting back to your question, from these considerations, since the speed of your object can only increase until it reaches terminal velocity, the two speeds must be equal provided the object achieves terminal velocity even if falls from the twenty foot ladder. In case the height is too small for the object to achieve terminal velocity then there can be a difference in speeds.

Power is not relevant here.

At any rate, I certainly enjoyed myself thinking about this question Brian

PS: Brian's comment:
Thanks, so i guess cartoons arent so right after all, heh. I always thought that the more it falls, to an infinant(spelling?) extent, the faster it goes. So i guess dropping a penny off the empire state building won't be as powerful as I thought. Oh well, i guess my science teacher was right.

(i) a) Yes and no. Yes it would be helpful to have a high density but need not always be. You can smash through mercury and lead but cannot do so easily with concrete and steel. By the same token you and I can withstand a large force a very fast moving ball has by learning to withdraw our hands as we catch the ball.

    b) You may want to read a little about snow that I'd answered elsewhere. In any case to address your question, your assumption relating snow's properties to its density is not true. It should follow from what we said above.

    c) You're making up new forces here Yang. One speaks of air resistance, weight, upthrust and so on. When a body falls the air resistance on the object is less than the weight until it reaches terminal velocity. At the terminal velocity, the weight = the upthrust, so that the object can fall at constant velocity according to Newton's first law.

(ii) I think you're once again getting stuck to the final outcome of the interaction. Netwon's third law is valid and more so AT THE INSTANT of the interaction. It is possible for one force to overcome some other. You do exert a force on the snow on account of your weight and the snow in return exerts an EQUAL force on you. Howwever your weight is able to push the molecules of snow apart and cause you to go down which may not always be the case. Get it?

Air resistance is NOT the force exerted by the body. It is the force acting ON the body. This could be equal to the weight during terminal velocity situations.

(i) I'd suggest that you read some of my answers above that address Newton's third law. They have my views on this law. Meanwhile I'd also like to suggest a sampler of URL's at different levels where you can access more information on this law.

    http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l4a.html

    http://www.lerc.nasa.gov/WWW/K-12/airplane/newton3.html

    http://www.iit.edu/~smile/ph9408.html

    http://www.iit.edu/~smile/ph9608.html

(ii) The EARTH experiences the reaction force to a body's weight in free fall.
According to Newton's third law,

"If body A exerts a force on body B, they body B will exert an equal force on body A along the same straight line in the opposite direction".

There are FOUR facts you can figure out from this statement of Newton's third law. That is, the two forces;

1. Come in PAIRS.
2. Are EQUAL in magnitude.
3. Would be pointing in OPPOSITE directions along the same straight line, and
4. Act on DIFFERENT BODIES.

The statement more popular in text books would be that to every action there is an equal and opposite reaction. This statement does not help you to understand the implications of the third law as delineated above.

The action in your case is the weight acting on the body undergoing free fall being attracted by the Earth. The reaction to this is the body attracting the Earth in its turn towards itself. You don't sense this attraction because the Earth is much too massive for you to see any appreciable change.

There are plenty of things one can speculate in theoretical physics and most of it is mathematical. To translate these into practical real life situation is always very difficult to conceive in our minds. The simple concept of four dimensions leave alone ten or more is difficult for us to imagine.

To make matters worse gravititational forces although most common are still the least understood of the four fundamental forces. Coming to your question on inertial dampers, I suggest you click on to these URL links on New Scientist to find some interesing opinions expressed in response to your question.

    http://www.newscientist.com/nsplus/insight/startrek/interactive_dampers.html

This is a classic problem that illustrates the concept of friction (try the sliding fingers on ruler activity).

Friction is an interesting force, because it has the following characteristics:

- it does not manifest unless you push or pull an object. Consequently, when no force is applied, the force of friction is zero
- if one does slowly apply a force and increases its value, the force of friction opposes the motion ant it too increases slowly increases in value until an object starts moving
- the maximum value of the force of friction is called the static friction and it is = μ_s N (where N is the normal force)
- once the object starts moving, the force of friction reduces to the kinetic friction which equals μ_k N
- if an object is actually moving at constant velocity, then the force of friction will be the kinetic friction

Now using these principles and the idea of weight and normal force, we can solve this problem.

First,

Weight = m x g

Assuming g = 10 m/s² we have here

Weight of box = 2.5 x 10 = 25 N

The normal reaction if the box is on a horizontal surface is N = W = 25 N

Therefore the force of static friction = μ_sN = 0.40 x 25 = 10 N, and
the force of kinetic friction = μ_kN = 0.20 x 25 = 5 N

(a) When the box is at rest and the monkey applies no force, the force of friction is zero.

(b) If the box is initially at rest and the monkey applies a force of 7.0 N, it is less than the static friction 10 N, and therefore the box will not move. This is because the opposing force of friction also increases to 7.0 N and the object does not move because the net force F_net is zero.

(c) The minimum force the monkey must apply to set the box in motion is the force of static friction = 10 N.

(d) The minimum force the monkey must apply to set the box in motion at constant velocity once it has been set in motion is the force of kinetic friction = 5 N.

(e) This problem is like like question 10. However, you must recongnize the with a force of 15 N, the box would obviously be moving and therefore you must use the kinetic friction.

The net force F_net = 15 - 5 = 10 N

Consequently, the acceleration a = F_net/m = 10/2.5 = 4 m/s²

(a) 0 N
(b) 7 N
(c) 10 N
(d) 5 N
(e) 4 m/s²

Draw a sketch because visualizing is the first step towards solving a problem.

We'll split the problem into two parts.

Part I (In Air)

(a) In the first part, the stone is falling toward the ground.

Since u, a & t are known, we can use the third equation of motion:

d= ut + 1/2at²

Substituting,

H = 1/2gt² (since u = 0, d = H & a = g)
= 1/2 (9.8)(3)² = 44.1 m (3 s.f.)

We can also calculate the velocity with which the stone will hit the ground using the first equation of motion:

v = u + at
v = gt (since u = 0 & a = g)
= 9.8 x 3 = 29.4 m/s

Part II (Inside Ground)

(b) The velocity with which the stone hits the ground will be its initial velocity for this part of the problem.

Therefore, u = 29.4 m/s
v = 0 (after the stone has penetrated the ground)
d = 9 cm = 0.09 m
a = ?

Using the fourth equation of motion:

v² = u² + 2ad, we have
0 = (29.4)² + 2(a)(0.09)
0 = 864.4 + 0.18a

Simplifying and solving,

a = -4802 m/s2

Using Newton's second law,

F = ma = (0.08)(4802) = 384 N

m = 50 kg
n = 13 students
Fs = 150 N per student

M = 80 kg
N = 5 parents
Fp = 475 N per parent

Again, draw a sketch of the system.

The weight of the 3 kg object = m₁g = 3 x 10 = 30 N and
the weight of the 2 kg object = m₂g = 2 x 10 = 20 N

Clearly, the object would accelerate in the direction of the 30 N force.

Let "a" be the acceleration of the system.

Looking at the free-body diagram for the 3 kg object, we have

30 - T = 3a (since it's moving down), and

for the 2 kg object,

T - 20 = 2a (since it's moving up)

Adding the two equations, you get

10 = 5a, or a = 2 m/s²

Using this value of acceleration in any one of the tension equations, say the first, we have

30 - T = 3(2) or T = 24 N