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Pengalaman Belajar Fisika di SMAN BI 1 Banjar

Buoyancy: Archimedes Principle

SUBJECT: Physics
TOPIC: Buoyancy
DESCRIPTION: A set of mathematics problems dealing with buoyancy.
CONTRIBUTED BY: Carol Hodanbosi
EDITED BY: Jonathan G. Fairman - August 1996

There are two types of flying machines that allow for lift to overcome gravity. The first type, called the aerodynamic machines such as helicopters and airplanes, rely on thrust and forward speed to produce lift. The second type, aerostatic machines, such as hot air balloons and lighter than air-type craft, rely on the differences in air density for lift.

This lesson is concerned with the second type, the type that are dependent on buoyancy.

If a cubic centimeter of aluminum was suspended in a fluid such as water with a very thin and negligible thread, the metal cube would have the fluid exerting pressure on the cube. Try to imagine that if the cube were to disappear, and the fluid would magically replace the cube, then the surrounding water would support this cube that is now containing water, so that the cube of water would be motionless. That is, the forces would be balanced. The cube of water would push out on the surrounding water and the surrounding water would push back on the cube. The fluid would be static, or stationary. Now replace this same cube of water with the original cube of aluminum. The surrounding water would not 'know' that the cube has been replaced with another substance. It would still push inward and upward and downward with the same force that it pushed on the cube of water. The sideways forces would be balanced and oppose each other equally, but the upward and downward forces would not be the same. The pressure at the bottom of the cube is greater than the pressure at the top of the cube, because pressure increases with increased depth. The difference between the upward and downward forces acting on the bottom and the top of the cube, respectively,is called buoyancy.

Using the aluminum as our example, it has a specific gravity of 2.8. Water has a specific gravity of 1.0. This means that a cubic centimeter of water would have a mass of 1.0 grams, while aluminum of the same size would have a mass of 2.8 grams. Since the aluminum cube displaces 1 cubic centimeter of water, it has a buoyancy of 1.0 grams. Since buoyancy is a force and not a mass, it must be converted to the proper units, which when multiplied by the acceleration of gravity (980 cm/s²) gives the units of dynes. That is,

(1.0 grams) (980 cm/s²) = 980 grams cm /s² or dynes

So our aluminum cube immersed in water would not 'weigh' (2.8 x 980) dynes or 2744 dynes. It would weigh less due to the fact it has a buoyant force of (1 x 980) dynes from the water. So it would weigh (2744-980) dynes or 1764 dynes while immersed in the water.

Archimedes Principle states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object.

Hot air balloons rise into the air because the density of the air (warmer air) inside the balloon is less dense than the air outside the balloon (cooler air). The balloon and the basket displaces a fluid that is heavier than the balloon and the basket, so it has a buoyant force acting on the system. Balloons tend to fly better in the morning, when the surrounding air is cool.

Exercises:

1. Find the weight of the air in a room with dimensions of 20 ft x 12 ft x 15 ft. The weight density of air at sea level is 0.08 pounds /ft³.
   (answer)
2. An iron anchor weighs 250 pounds in air and has a weight density of 480 lbs/ft³. If it is immersed in sea water that has a weight density of 64 lbs/ft³, how much force would be required to lift it while it is immersed?
   (answer)
3. An aluminum bar weighs 17 pounds in air. How much force is required to lift the bar while it is immersed in gasoline? The weight density of aluminum is 170 pounds /ft³ and that of gasoline is 42 pounds /ft³.
   (answer)
4. How much does a 20 ft x 10 ft x 8 ft swimming pool filled with water weigh? Assume the water has a weight density of 62 lbs/ft³.
   (answer)
5. A balloon weighing 80 kg has a capacity of 1200 m³. If it is filled with helium, how great a payload can it support? The density of helium is 0.18 kg/ m³ and the density of air is 1.30 kg/ m³. Express your answer in newtons.
   (answer)

 Sumber:

NASA

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Pengalaman Belajar di SMAN BI 1 Banjar

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Newton's Third Law of Motion

SUBJECT: Physics
TOPIC: Force and Motion
DESCRIPTION: A set of mathematics problems dealing with Newton's Laws of Motion.
CONTRIBUTED BY: Carol Hodanbosi
EDITED BY: Jonathan G. Fairman - August 1996

The third law of motion states that if a body exerts a force on a second body, the second body exerts a force that is equal in magnitude and opposite in direction to the first force. So for every action force there is always a reaction force. No force can occur by itself

The book lying on the table is exerting a downward force on the table, while the table is exerting an upward reaction force on the book. Because the forces are equal and opposite, the book remains at rest. Notice also that the table legs are in contact with the floor and exert a force downward on it, while the floor in turn exerts an equal and opposite force upward.

Questions for you to consider:

If forces are always equal and opposite in action and reaction, how is it possible for an object to accelerate?
(Answer)

Explain, in detail, using the third law of motion, how a person is able to walk forward.
(Answer)

There is a classic problem that physicists like to ask students. A horse is pulling a carriage on a level ground. The horse knows the third law of motion. He tells the carriage that he will exert a force forward, and the carriage will exert a force equal to the horse's force but in opposite directions. Therefore, the horse explained, he can never pull the carriage forward. Can you explain to the horse that he is mistaken? How is he able to pull the carriage forward?
(Answer)

Sumber:

NASA

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Pengalaman Belajar Fisika di SMAN BI 1 Banjar

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The First and Second Laws of Motion

SUBJECT: Physics
TOPIC: Force and Motion
DESCRIPTION: A set of mathematics problems dealing with Newton's Laws of Motion.
CONTRIBUTED BY: Carol Hodanbosi
EDITED BY: Jonathan G. Fairman - August 1996

Newton's First Law of Motion states that a body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force.

If a body experiences an acceleration ( or deceleration) or a change in direction of motion, it must have an outside force acting on it. Outside forces are sometimes called net forces or unbalanced forces.

The property that a body has that resists motion if at rest, or resists speeding or slowing up, if in motion, is called inertia. Inertia is proportional to a body's mass, or the amount of matter that a body has. The more mass a body has, the more inertia it has.

The Second Law of Motion states that if an unbalanced force acts on a body, that body will experience acceleration ( or deceleration), that is, a change of speed. One can say that a body at rest is considered to have zero speed, ( a constant speed). So any force that causes a body to move is an unbalanced force. Also, any force, such as friction, or gravity, that causes a body to slow down or speed up, is an unbalanced force. This law can be shown by the following formula

F= ma

• F is the unbalanced force
• m is the object's mass
• a is the acceleration that the force causes

If the units of force are in newtons, then the units of mass are kilograms and the units of acceleration are m/s². If the units of force are in pounds (English), then the units of mass are in slugs, and the units of acceleration are ft/s².

Motion of an object that is not accelerated (moving at a constant speed and in a straight line) can be found using the formula

d= v t

• d is the distance traveled
• v is the rate of motion (velocity)
• t is the time

Some sample problems that illustrates the first and second laws of motion are shown below:

Example 1
If the speed of sound on a particular day is 343 m/s, and an echo takes 2.5 seconds to return from a cliff far away, can you determine how far the cliff is from the person making the sound?

An echo is a sound that travels out and back. It take 2.5 seconds for this trip, which is twice the distance to the cliff. Therefore, it only takes 1.25 seconds for the sound to reach the cliff. By substitution,

d = v t
d = (343 m/s) (1.25 s)
d = 429 m

Example 2
If an unbalanced force of 600 newtons acts on a body to accelerate it at +15 m/s², what is the mass of the body?

F = ma
m=F/a
m = 600n/15 m/s2
m= 40 kg

Exercises:

1. If a car is traveling at 50 km/hr along a straight line, how many meters does it travel in 10 seconds?
   (Answer)
2. A force of 5000 newtons is applied to a 1200 kg car at rest. What is its acceleration?
   (Answer)
3. A 10 kg body has an acceleration of 2 m/s². Find the net force acting on the body.
   (Answer)
4. An empty truck with a mass of 2500 kg has an engine that will accelerate at a rate of 1.5 m/s². What will be the acceleration when the truck has an additional load of 1500 kg ?
   (Answer)
5. A box resting on a table has a mass of 5.0 kg.
   1. What is its weight?
   2. What will be its acceleration when an unbalanced horizontal force of 40 newtons acts on it?
      (Answer)
      
      
6. What is the weight of an object that has a mass of 60 slugs?
   (Answer)
7. A net force of 75 pounds acts on a body of 25 slugs. The body is initially at rest. What is its acceleration during the action of the force?
   (Answer)
8. What is the mass of a 185 pound man? If a 100 pound horizontal net force acts on the man while he is sitting on a wooden floor, what will his acceleration be?
   (Answer)