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1. Newton's First Law of Motion Three fundamental principles, called Newton's First, Second and Third Laws, form the basis of classical, or Newtonian, mechanics and have proved valid for all mechanical problems not involving speeds comparable with the speed of light and not involving atomic or subatomic particles. Newton's First Law states that a particle not subjected to external forces remains at rest or moves with constant speed in a straight line. This is also known as the Law of Inertia. Newton's first law of motion is often stated as: An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. 2. Newton's Second Law of Motion The second law is the one that tells you how to calculate the value of a force. Force (measured in Newtons) is one of the fundamental physical properties of a system and comes in many forms. You might feel it as a push or pull (a mechanical force), while it is the value of your weight (the gravitational force of the Earth pulling on you) and can be seen in the repulsion or attraction of magnets or electric charges (electromagnetic force). The Law is often stated as: The acceleration of a particle is directly proportional to the resultant external force acting on the particle and is inversely proportional to the mass of the particle, or a = F/m. 3. Newton's Third Law of Motion If two particles (or bodies) interact, the force exerted by the first particle on the second particle (called the action force) is equal in magnitude and opposite in direction to the force exerted by the second particle (called the reaction force). Suppose you are watching the lift off of a rocket, like the ones by SpaceX. You hear a deafening roar and see burning gases shooting from the exhaust vents of the rockets. At that moment, the rocket moves slowly upward. You can infer that the force for the lift off comes from the burning gases pushing against the shuttle rockets. Why does the shuttle system move in the opposite direction of the gases? The forces on the rocket are similar to the forces in a collision between two tennis balls. When the balls collide, they are propelled in opposite directions. The rockets force burning gases downward through the exhaust vents. In response to these downward forces, the shuttle system moves upward. The motion of the rocket demonstrates Newton's third law of motion. When one object exerts a force upon a second object, the second object exerts an equal and opposite force upon the first object. The third law of motion states that every action has an equal and opposite reaction. You can see equal and opposite forces interact when you blow up a balloon and release it, it moves in the opposite direction. The force propelling the balloon is equal and opposite to the force of the air leaving the balloon. 4. Newton's Law of Universal Gravitation Newton's Law of Universal Gravitation states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. 5. Einstein's Special Theory of Relativity Einstein's theory about the relationship between space and time is based on two postulates: (1) that the laws of physics are invariant in all inertial systems and (2) that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. 6. Zeroth Law of Thermodynamics The principle states that if two bodies are each in thermal equilibrium with a third body, then the first two bodies are in thermal equilibrium with each other. 7. First Law of Thermodynamics
The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.
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The volume of a 3 dimensional solid is the amount of space it occupies. â€‹
Since the end (base) of a cylinder is a circle, the area of that circle is given by the formula:
\[area = Ï€ r^2\]
The volume of a cylinder is found my multiplying the area of one end of the cylinder by its height. So the formula of the volume of a cylinder is:
\[volume = Ï€ r^2 h\]
where:
Ï€ is Pi, approximately 3.142 r is the radius of the circular end of the cylinder h height of the cylinder
Our problem involves calculating the volume of Amazon Echo. The height of the Echo is 235mm while the diameter of the base is 84 mm or 8.4cm . Let's first find the area of the base.
The area of the base of Amazon Echo is:
\[area = Ï€ r^2\]
\[= 3.142 x 8.4^2\]
= 221.56 cm^2
To calculate the volume, we multiply the area with the height of the Echo, which is 235mm or 23.5cm
So, volume of Alexa Echo = 221.56 * 23.5 = 5,206.6224 cm^3
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The GMAT is a tricky test, so make sure you can solve the easy problems. Test yourself with the following problems. Questions1. The value of an investment triples every 10 years. By what factor does the value increase over a 30year period? (A) 3 (B) 6 (C) 9 (D) 27 (E) 30 2. A chemist is making a 50% alcohol solution. How many milliliters of distilled water must the chemist add to 600 milliliters of an 80% alcohol solution to obtain a 50% solution? (A) 180 (B) 300 (C) 360 (D) 480 (E) 600 3. An investor receives interest on two simple interest investments, one at 3%, annually, and the other at 2%, annually. The two investments together earn $900 annually. The amount invested at 3% is $20,000. How much money is invested at 2%? (A) $10,000 (B) $12,000 (C) $15,000 (D) $20,000 (E) $35,000 4. If the diameter of a circle is 14, then the area of the circle is
(A) 7pi (B) 14pi (C) 28pi (D) 49pi (E) 196pi
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Question 1: An astronomer discovers a planet with two moons. One moon is 2 times as far from the center of the planet as the other and 3 times the mass of the other moon. What is the ratio of the gravitational force on the first moon to the gravitational force on the second moon? (A) 0.33 (B) 0.40 (C) 0.66 (D) 0.75 (E) 0.90 Question 2: A 1newton force and a 4newton force act in opposite directions. What is the magnitude of the resultant force, in newtons? (A) 0 (B) 1 (C) 3 (D) 4 (E) 5 Question 3: An object starts from rest and accelerates at 6.0 m/s^2 for 4.0 seconds. How far does it travel? (A) 8.0 m (B) 12 m (C) 48 m (D) 96 m (E) 288 m Question 4: Force A and Force B act on an object. Let theta equal the angle between the directions of the two forces. At what value of theta is the resultant force the greatest?
(A) 0 deg (B) 45 deg (C) 60 deg (D) 90 deg (E) 180 deg 