Mechanics 1

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1. Do falling objects drop at the same rate (for instance a pen and a ball dropped from the same height) or do they drop at different rates? I know a feather floats down very slowly but I would think a heavy object would fall faster than a light object.

In presence of air resistance, two bodies of different masses dropped at the same rate from the same height reaches the ground at different time. The weight of the body acts on downward direction whereas the force of air resistance acts upward. For light object, the force of air resistance is greater but for the heavier object, it is lesser. So, the heavier objects fall faster than a light object in presence of air resistance. Hence, a feather floats down very slowly but a heavy object fall faster than a light object.

While if two bodies of different masses dropped at the same rate from the same height in the vacuum then both will reach the ground at the same time as there is no force of resistance which acts on that bodies.

2. Why can a person lie on a bed of nails and not be injured? What is this scientific theory called?

This is a trick used by most tricksters and the so called magicians. But it is a feat that can be performed by all. A bed of nails has a lot of them, more than hundred. When a person lie on it, his/her weight (downward force) is distributed over the tips of all of them, increasing the area of contact. So by the relation , the body surface will feel less pressure. The harm on the body, then will be obviously less. If the same action be done on a single nail, then see if the magic works or not!!

3. I know that gravity keeps us on the earth, but what prevents us from being pushed or pulled through the floor, earth, etc. (besides concrete, wood, and soil)? Does it have something to do with opposite forces?

Newton's law of gravitation states that "the force of attraction between any two bodies in this universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between them".

Hence, the mass of the earth is infinitely greater than mass of us. Hence, the force of attraction between the earth and us is quite much bigger than the force of attraction between us & any other substances. So the resultant effect is that all the substances are pushed into the ground. The question is why not through the ground right into the center of the earth.

The phenomena is prevented by yet another significant phenomena on earth. That is the electrostatic force existing between any charged particle. As a person touches the ground, the electrons of the outermost atoms of the body will be in direct contact with the electrons of the outermost atoms of the ground. The decrease in their separation brings an increase in the electrostatic repulsive force in between them. So this force starts to act against the force of gravity, and puts the body in balance.

However, as in the case of water, if they are themselves weak enough to exert any such opposing forces, the bodies sink into them.

4. Can you compress a liquid (water)?

The question is very much against something students are taught at their junior level that liquids are incompressible and gases are. The terminology used here is a comparative term. There is no substance that can not be compressed if sufficient force is applied. It is not the matter whether the substance can be compressed or not. The core is whether there exists enough force to produce that compression. An ant might not be able to squeeze an air filled balloon, but humans can. So the balloon is incompressible for the ant but compressible for humans.

Similar is the case of liquid compression. A small force ensures the compression of gases, but liquid compression requires a lot of force. How this force is created is however impracticable in normal life and normal measuring instruments might not be able to measure them. Seeing nothing in a dirty glass does not mean that there are no germs.

5. How do you determine the distance of lightening from where you are standing using the sight of lightening and the sound of the thunder?

Light travels at approximately 186,000 miles per second while sound travels at approximately 1100 ft. per second.

Considering the time it takes the light to reach you being negligible (because of such a high speed of light), when you see the lightning flash start counting at a per second rate then when the thunder is heard multiply your count by 1100 and this will give an approximation of the distance in feet from you to the lightning.

6. Why do your ears pop when you are in an airplane?

The outside of the eardrum is exposed to the pressure of the air where ever you may be located. That pressure is 14.7 pounds per square inch at sea level on a standard day.

The space inside of the eardrum is usually at the same pressure as the outside. This is facilitated by a tube; one end of which opens into the space of the 'inner ear' and the other end opens into the rear part of your throat. But, that end of the tube is normally lightly squeezed closed. Each time you swallow or yawn it opens just enough to admit air to the inner ear, thereby equalizing the pressure with the outside. Your ear drum then feels comfortable.

When you climb higher as in an airplane or in a car in the mountains, you are going into an area of lesser air pressure. The air from the lower altitude is 'trapped' in the inner ear. If it can not escape you will soon have an ear ache caused by the ear drum being ballooned outward (stressed) by the higher pressure inside. So, it pushes out through the 'Eustachian tube' into your throat with bubble-popping sound.

If you have an infected throat, the tube opening may be swollen closed and the inner ear pressure cannot be equalized without resulting in eardrum pain. You have to swallow hard and yawn to assist in opening the tube to let the pressure escape. Likewise upon descent, if the higher pressure at lower altitudes can not pass into the inner ear, pain will result. NEVER, repeat: NEVER hold your nose and blow in order to clear your ears. If your throat is infected you will blow infectious mucus into your inner ear, causing an infection there. Instead, swallow hard several times to 'wipe' clear the opening of the Eustachian tube, then immediately yawn and stretch your jaw forward in repeated efforts to open the tube enough to equalize the pressure.

7. What is the physics involved in skydiving?

There is quite a bit of physics involved in skydiving, but lets start with the basics. Once you leave the plane there are essentially only two forces acting on you: the Earth's gravity pulling you straight down, and friction with the air. The friction with the air mostly adds up to push in the opposite direction from the direction you are moving, so basically it pushes up on you and your equipment.

Air resistance increases as your speed increases, so when you first start dropping and are moving slowly, gravity is stronger than the air resistance and you speed up, accelerating towards the ground. However the faster you drop, the stronger the air resistance is and so eventually you are moving so fast that the air resistance is equal in strength to gravity and you don't accelerate any more. You have reached terminal velocity for your current body position.

Why does body position come into it? Because air resistance also depends on the shape of the object (you) and so by tucking in your arms and legs you can reach a faster terminal velocity than if your arms and legs are spread out. But skydivers don't splay their arms and legs to slow down per se (if they were afraid of high speeds we can imagine they would have chosen a different sport). They are trying to achieve a position of dynamic stability.

Dynamic stability is what allows an arrow to fly nose first. If the arrow starts to flip sideways, the air resistance against the fletching is greater than the resistance at the nose, and the arrow automatically goes back to its initial orientation. Likewise, skydivers don't want to be tumbling end over end and out of control, so they trail their arms and feet behind them to act like the feathers on the arrow.

There are lots of things going on in skydiving. The things you are probably trying to ask are, 'How can skydivers do the things they do in the sky?' or, 'How can they land safely using a parachute when they are flying at high speeds?'

There is one simple answer. Air resistance. When a mass is moving at speeds like that, air resistance causes them to slow/speed their velocity by their position. If they were in a diving position ' V ' , there is less air resistance, because there is less surface area facing the direction you are going in. If you were to spread all of your limbs out, it causes a much greater surface area, causing more air to collide with your stomach, slowing you down.

As for parachutes, it needs to cover a wide enough surface area in order to cause enough air resistance to slow the mass down dramatically, that's why a huge snap up occurs when you release your parachute, the huge amount of added air resistance at one time causes such a dramatic slow down. BUT! Circular parachutes need a small hole at the tip in order to prevent a flip around. Air doesn't WANT to be resisted, so it tries its best to cause the smoothest path possible, even if it needs to flip that parachute. So, the hole on top causes a smaller chance of that, but air coming up from that hole is immense. So, the easiest solution is a square shaped parachute. It provides the needed air resistance, without the excess area it covers due to its circular shape. Also, it allows skydivers to "steer" their way to a good landing.

8. If there was a hole through the earth would you be stopped in the middle due to gravity or would you fall straight through?

All objects are attracted to the centre of the Earth.

If the hole runs through the centre it will be rather like pulling a pendulum to one side and allowing it to settle, the pendulum oscillating back and forth. Thus you would fall in a straight line accelerating towards the centre then decelerating away from the centre until you, almost reach the other side of the earth and your velocity is zero. Then you will be drawn back, accelerating and decelerating again, to almost where you originally fell. Each journey back and forth like the pendulum gets shorter and shorter until you settle stationery at the centre of the earth. This is due to the fact that there is air in the hole which provides friction or drag. Such motion is called Damped Harmonic Motion (if the hole was in vacuum then your would not settle at the centre but would continue to execute a full simple harmonic motion)

Holes not going through the centre have similar effects but you would fall in a curve and bump the side of the hole half way down, as the earth tries to attract you to its centre. You will again end up half way down the hole but stuck to the side which is closest to the earth's centre.

9. What is a geo-stationary orbit? Are there any other orbits?

A geo-stationary orbit is an orbit of an Earth's satellite whose period of rotation is exactly equal to the period of rotation of Earth about it's polar axis (which is 23 hours, 56 minutes and 4.1 seconds) and whose trajectory is aligned with the Earth's equator.

Any satellite in this orbit will appear as if it is always in the same place in the sky when observed from the same point on the Earth. This orbit is at a distance of approximately 35,900 km from the surface of the Earth. Communication satellites are usually placed into this orbit, with several satellites in the same orbit, distributed around to provide world wide coverage for relaying the telecommunication signals.

A geo-stationary orbit is also sometimes called: stationary, or synchronous orbit.

10. An astronaut in a circling satellite released an object out of the satellite in space. Will this object fall on the earth? Explain.

The object will not fall on the earth. Due to inertia of motion, the speed of the released object will be equal to the speed of the satellite in all respects, which makes this velocity equal to the orbital velocity. This velocity does not depend on the mass of the satellite, so it will follow the motion of the satellite and will act as another satellite of the earth.

11. Where is the force of gravity stronger, on the top of Mt. Everest or at sea level?

The force of gravity is stronger at sea level. The gravitational force, as explained by Newton's Law of Gravitation, is inversely proportional to the square of the separation between the two masses (or the separation between the centers of mass for the two objects).

In the case of the earth, the force of gravity is greatest on its surface and gradually decreases as you move away from its centre (as a square of the distance between the object and the center of the Earth). Of course, the earth is not a uniform sphere so the gravitational field around it is not uniform. Instead the force of gravity will also vary according to the mineral or oil deposits underground. There is also a need to distinguish between 'gravitational acceleration' and 'acceleration of free fall' of which we are more interested in. In the case of the latter, the latitude of the place we are concerned with also matters because of the rotation of the planet.

12. As an engineer, I know that friction does not depend upon surface area. As a car nut, I know that wider tires have better traction. How do you explain this contradiction?

This is a good question and one which is commonly asked by students when friction is discussed. It is true that wider tires commonly have better traction. The main reason why this is so does not relate to contact patch, however, but to composition. Soft compound tires are required to be wider in order for the side-wall to support the weight of the car. softer tires have a larger coefficient of friction, therefore better traction. A narrow, soft tire would not be strong enough, nor would it last very long. Wear in a tire is related to contact patch. Harder compound tires wear much longer, and can be narrower. They do, however have a lower coefficient of friction, therefore less traction. Among tires of the same type and composition, here is no appreciable difference in 'traction' with different widths. Wider tires, assuming all other factors are equal, commonly have stiffer side-walls and experience less roll. This gives better cornering performance.

Another Answer
Friction is proportional to the normal force of the asphalt acting upon the car tires. This force is simply equal to the weight which is distributed to each tire when the car is on level ground. Force can be stated as Pressure × Area. For a wide tire, the area is large but the force per unit area is small and vice versa. The force of friction is therefore the same whether the tire is wide or not. However, asphalt is not a uniform surface. Even with steamrollers to flatten the asphalt, the surface is still somewhat irregular, especially over the with of a tire. Drag racers can therefore increase the probability or likelihood of making contact with the road by using a wider tire. In addition a secondary benefit is that the wider tire increased the support base and makes it hard to turn the car over in a turn or in a mishap.

13. A car is traveling at 60mph collide with another car traveling in same direction. If instead it collides into a wall at 60mph. Which one has more damage?

The magnitude of damage depends upon force received by a car when it collides with another car or wall. If the magnitude of force is greater then there is more damage and vice-versa. The force F received by a car when it collides with another car or a wall is given by the relation: , (where, dP is the change in momentum and dt is the time taken for collision).

When a car collides into a wall at 60mph then the change in momentum takes place in very short interval of time. As a result it receives greater force. When a car collides with another car traveling in same direction then the change in momentum takes place in longer interval of time so, it receives less force than former. If a car is traveling at 60mph collide with another car traveling in same direction. If instead it collides into a wall at 60mph. Latter one has more damage.

14. If Newton's law of motion, which states that any object in motion will remain in motion, is true, then why is it that as a comet gets close to the sun and it melts, and a tail forms, and why wouldn't it be just a big ball of melted stuff?

Newton's First Law of Motion actually states that a body in motion will remain in motion UNLESS ACTED UPON BY AN OUTSIDE FORCE. In the case of a comet, there are a number of outside forces acting upon it.

The primary force on a comet, of course, is gravitational as it orbits the Sun. That force, however, acts more or less uniformly on all parts of the comet (ignoring tidal forces). Other forces, however, include the Solar Wind (a stream of subatomic particles emitted by the Sun) and sunlight itself. While these forces are small and have little effect on the large mass of the comet, they are large enough to influence the smaller mass of its tenuous tail. The small particles of dust and gas that form as the comet's material is heated near the sun are 'blown' outward, away from the sun and the comet's main body, because their small mass is more easily accelerated by the small forces mentioned above.

15. I was told by my Physics instructor that there is such a thing as negative time. Is that true, or was he just pulling my leg?
Physics teachers never pull the legs of their students. Most especially this one and I am sure yours never has either. In fact we have to take an oath which says that we promise, for the whole of our teaching career to never ever pull the legs of our students. Gosh, if we ever pulled a students' leg we could lose our Physics License.

So, yes, there is such a thing a negative time. Think about the launch of the Shuttle. You will hear the announcer saying 'T minus three minutes to launch.' This means exactly what it sounds like: minus time! Now, what does negative time mean? Simply this: the time before you are actually measuring the time for the experiment or the measurement. For example, if your class was doing an experiment where you had to collect data on how fast a ball rolled down a ramp you might want to give your timekeeper some notice before you start the ball rolling so that she will be able to start the clock at exactly the same time you roll the ball. So, you might say, 'Three, two, one, now!' Well, this is negative time.

I hope this answer helps. And remember, Physics Teachers never pull the legs of their students!

16. Does a car makes more pressure to the floor when it goes faster, or the car could fly if it goes even faster?

What an interesting question. This kind of question shows that you are thinking because on the one hand it seems to make sense that the faster a car goes the harder it must push on the floor to go fast. But on the other hand it doesn't quite sound right. So, this kind of question shows that you are thinking about what you are thinking and that is always a good thing to do.

OK, now to answer your question. The pressure the car applies to the floor is a function of the weight of the car and area of the car's tires. The equation P=F/A is the equation. This pressure cannot change unless either the weight or the area of the tires changes. Do you think that by going faster that either of these two things can change? Under normal conditions, the answer is 'no'. Whatever the car weighs it weighs the same no matter how fast it goes. Whatever the area of the tires that are on the ground will also stay the same no matter how fast the car goes. But, all of this is only under normal conditions.

Some cars have spoilers on the back end. Do you know that these are supposed to do? Well, if a car goes fast enough and if the spoiler is designed correctly the car will have the opposite of what an airplane has to make it fly. Call it anti-lift. The shape of the spoiler causes the car to have more weight sue to the flow of air over the spoiler. So, the faster the car goes the less chance it has of flying. Do you think you could turn the spoiler upside down and get lift like an airplane? You could do this but the lift would not be nearly enough to raise the car off the ground.

Now, you may have seen movies where cars that go very fast seem to fly off the ground. This is precisely because they are going so fast. As Newton's first law states: An object in motion will stay in motion in a straight line at a constant velocity unless an unbalanced force acts upon it. Cars that go very fast and also go up a short incline will keep going up after they have passed the end of the incline and since the velocity is so high they will travel a long distance before coming back to the ground. They are not flying because of their great speed so much as because of their great inertia combined with speed over a ground that falls away giving the illusion of having flown.

17. Why is simple harmonic motion 'simple'? Is there a complex harmonic motion?

If you look at a text on Simple Harmonic Motion in a physics book you see that 'Simple' refers to the ideal case where there is no friction, viscosity etc. Indeed, ideal cases are usually the simples in Physics. But many books also have parts on 'Damped Oscillations' and 'Forced Oscillations' but these are not considered as simple, because they are closer to real cases. Also the solutions to ideal case is the simplest, and the solutions to forced and damped oscillations are more complicated as one could expect.

18. Why doesn't friction depend on surface area?

Although a larger area of contact between two surfaces would create a larger source of frictional forces, it also reduces the pressure between the two surfaces for a given force holding them together. Since pressure equals force divided by the area of contact, it works out that the increase in friction generating area is exactly offset by the reduction in pressure; the resulting frictional forces, then, are dependent only on the frictional coefficient of the materials and the FORCE holding them together.

If you were to increase the force as you increased the area to keep PRESSURE the same, then increasing the area WOULD increase the frictional force between the two surfaces.

19. A pendulum is hanging in a lift and is oscillating. The lift is given a free fall. What will happen to the bob of the pendulum?

It depends on the time when free fall starts. The bob will continue to move it's angular motion without any change in its angular speed -so the angular momentum- with respect to freely falling lift.

At this point (start of free falling) there is no gravity force felt inside the lift. So you can imagine it like a room in space where there is no gravity. Since there is no gravity, there is no external force acting on pendulum other then the force acting on its pin due to circular motion (due to acceleration towards the origin), but this force doesn't change the angular momentum w.r.t. pin because it's acting on the pin where the radius is zero.

So, we have two cases for the angular momentum just before free falling; angular momentum is zero or not.

First Case: Just before free falling, the pendulum is at its widest angle (highest point), where the angular velocity is zero. It's at rest instantaneously. It continues to stay at this position with respect to lift. (Until the lift crashes when it hits to ground )

Second Case: Just before free falling, the angle of pendulum is at some angle other then the maximum, where it has some speed. It continues to rotate with this -constant- angular speed while free falling until it hits the ceiling.

20. According to Newton's third law, every force is accompanied by an equal and opposite force. How can a moment ever take place?

Moment is the 'rotating effect' of force. A body rotates or feels a moment when two forces are acting on it but are not in the same line, I.e. there is some distance between the lines of action of the two forces. However if they are acting directly against each other in the same line, they simply cancel or undermine each other and thus produces no moment.