Physics: Gravity and Newton's Laws

Gravity

• Gravity is a force of attraction between any two objects in the universe.
• The strength of the gravitational force depends on:
  • The mass of the objects: Larger objects have greater gravitational forces.
  • The distance between the objects: More distance reduces the gravitational force.
• Gravity is the weakest force among four fundamental forces in the universe.
• The Earth pulls all objects towards its center due to its gravitational force.
• The Earth's attraction is called the force of gravity, which causes objects to fall to the ground.
• Objects with higher mass experience larger forces of attraction.
• The universal law of gravitation describes the relationship between the masses of objects, the distance between their centers, and the force of gravity between these objects.

Newton's Laws of Motion

• Newton's first law of motion (the law of inertia) states that an object at rest stays at rest and an object in motion stays in motion with the same velocity unless acted upon by an unbalanced force.
• Newton’s second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass.
• Newton’s third law of motion states that for every action, there is an equal and opposite reaction.

Centripetal Force

• Centripetal force is a force that acts on an object moving in a circular path, directed towards the center of the circle.
• Centripetal force is necessary to keep an object moving in a circular path.
• The Moon orbits the Earth due to the Earth’s gravitational force, which acts as the centripetal force keeping the Moon in orbit.

Tangent

• A tangent is a line that touches a circle at exactly one point.
• If the centripetal force is removed, an object moving in a circular path will move along the tangent to the circle at the point of removal.

The Universal Law of Gravitation

• The Universal Law of Gravitation formula is: F = Gm₁m₂ / r² where
  • F is the force of gravity
  • G is the gravitational constant
  • m₁ and m₂ are the masses of the two objects
  • r is the distance between the centers of the two objects.
• The Law states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Additional Key Concepts

• An object's weight is directly related to gravitational force.
• The Earth-Moon gravitational attraction causes tides.
• Gravity is essential for life on Earth.

Universal Law of Gravitation

• The universal law of gravitation explains the attractive force between any two objects with mass.
• Scientists like Isaac Newton contributed to this law.
• This law helps us understand the attractive force between objects.
• Understanding mass and distance is key to understanding the attractive force between two objects.
• The force of attraction is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers.
• This relationship yields the formula: F = Gm₁m₂/r².
• F represents the force of attraction (in Newtons),
• G is the universal gravitational constant (a constant value),
• m₁ and m₂ are the masses of the two objects (in kilograms), and
• r is the distance between their centers (in meters).
• The gravitational constant is 6.67 x 10^-11 Nm²/kg².
• This value remains constant throughout the universe.
• Gravity acts upon any object with mass, irrespective of its size or location.

Key Points:

• Universal gravitation describes how every object attracts every other object proportionally to their masses and inversely to the square of their separation.
• This applies to any two objects with mass, regardless of their size or location.
• Examples include the Moon's orbit around Earth, planets orbiting the sun, and tides.

Applications:

• Universal gravitation explains why objects are attracted towards Earth.
• It explains the Moon's orbit around Earth and the planets' orbits around the Sun.
• It explains the tides caused by the Moon's gravitational pull.

Importance:

• Earth's gravitational pull: Explains why objects stay grounded on Earth.
• Moon's orbit: Explains the Moon's path around Earth.
• Planets' orbit: Explains the planets' paths around the Sun.
• Tides: Explains the tides caused by the Moon's gravity.

Formula and Calculation:

• The formula for gravitational force is: F = Gm₁m₂/r².
• G represents the universal gravitational constant.
• The value of G is 6.67 × 10⁻¹¹ Nm²/kg².

Example:

• Doubling the mass of an object doubles the force of attraction.
• Doubling the distance between objects reduces the force of attraction to one-fourth.

Force Of Gravitation

• Doubling an object's mass doubles the gravitational force.
• Doubling the distance reduces the gravitational force by a factor of four.
• Decreasing mass reduces the gravitational force.
• Increasing distance reduces the force.
• Decreasing distance increases the force.

Free Fall

• Free fall occurs when an object falls solely under the influence of gravity.
• Velocity increases continuously during free fall due to constant acceleration.
• Acceleration due to gravity (g) is approximately 9.8 m/s².
• 'g' varies based on planetary mass and radius.
• Acceleration due to gravity on the Moon is roughly 1/6th of Earth's.

Weight

• Weight is a force measured in Newtons (N).
• Weight is Earth's pull on an object.
• Weight calculation: Weight = mass × acceleration due to gravity (W = mg).
• Objects weigh less on the Moon due to its weaker gravity.

Motion of Objects Under the Influence of Gravity

• Two scenarios:
  • Throwing upwards: Initial velocity is positive, final velocity is zero at maximum height.
  • Dropping downwards: Initial velocity is zero, and the object accelerates downwards.
• Acceleration due to gravity is always downward: -g in upwards motion, +g in downwards motion.
• Three equations of motion:
  • v = u + at
  • s = ut + ½at²
  • v² = u² + 2as

Key Points to Remember

• The formula for gravitational force is F = Gm₁m₂/r².
• G is the universal gravitational constant; m₁ and m₂ are the masses of the objects; and r is the distance between their centers.
• Acceleration due to gravity at the poles is greater than at the equator.
• Earth is not a perfect sphere; it's slightly flattened at the poles.

Acceleration Due to Gravity

• Upward motion involves negative acceleration due to gravity's downward direction.
• Upward motion time is the time of ascent.
• Upward displacement equals the maximum height.
• Downward motion starts with zero initial velocity.
• Final velocity is never zero when moving downwards.
• Time of ascent equals time of descent.
• Acceleration due to gravity in upward motion = -g, downward motion = +g.
• Downward displacement = height.

Force of Gravitation

• An apple's force on Earth equals Earth's force on the apple (Newton's Third Law).
• Gravitational force exists between any two objects, regardless of their masses. However, the effect varies with the object's mass.
• A 10-Newton object on Earth weighs about 1.6 Newtons on the Moon due to the Moon’s weaker gravity.
• Gravitational force is constant for a given distance.

Key Formulas

• Acceleration due to gravity formula: a = g
• Force of attraction formula: f = Gm₁m₂ / d²
• Pressure formula: p = f / A

Thrust and Pressure

• Thrust is any force perpendicular to a surface. Unit: Newton (N).
• Pressure is force per unit area. Unit: Pascals (Pa) = N/m².
• Pressure is inversely proportional to area; larger area means less pressure.
• Pressure is directly proportional to force; more force means more pressure.

Pressure in Fluids

• Fluids (liquids and gases) exert pressure in all directions.
• Pressure at a given depth in a fluid is the same in all directions.
• Submerged objects experience pressure from the fluid.
• Fluid pressure on a surface is called fluid pressure.

Buoyancy

• Buoyancy is the upward force on a submerged object in a liquid or gas.
• Buoyancy equals the weight of the displaced fluid.
• Buoyancy helps objects float.
• Buoyancy acts opposite to gravity.
• Objects float if buoyancy exceeds gravity; sink if buoyancy is less than gravity.