Motion, Force, and Gravitation Relate to Mass & Weight
An object may appear to be at rest or in motion depending on the observer’s frame of reference. For example, passengers inside a moving bus see each other at rest, but an observer outside sees them in motion.
Types of Motion :
- Straight-line motion
- Circular motion
- Rotational and vibratory motion
- Uniform motion: Equal distances in equal time intervals.
- Non-uniform motion: Unequal distances in equal time intervals.
Key Concepts:
- Distance is the total path covered.
- Displacement is the shortest straight-line distance from initial to final position.
- Speed: Distance traveled per unit time. SI unit is m/s. Average Speed = Total distance / Total tim
- Velocity: Speed with direction. Can be uniform or variable. Average Velocity = (u + v) / 2
- Acceleration: Rate of change of velocity. SI unit is m/s². a = (v-u)/t
Equations of Motion
- v = u + at
- s = ut + (1/2)at²
- v² = u² + 2as
Where, u: Initial velocity, v: Final velocity, a: Acceleration, t: Time, s: Displacement
Historically, it was believed that rest is the natural state of objects. Galileo Galilei and Isaac Newton challenged this idea and introduced a new approach using the concept of force.
- The SI unit of force is newton (N), where 1 N = 1 kg·m/s².
Balanced and Unbalanced Forces
- Balanced Forces: Equal and opposite forces cancel out; no movement occurs.
- Unbalanced Forces: Unequal forces cause motion in the direction of the stronger force.
Law of Motion
- The Law of Inertia (First Law)
- The Law of Acceleration (Second Law) unbalanced force changes the momentum of an object. Momentum is defined as p=mv, (where m is mass and v is velocity). The rate of change of momentum is proportional to the force applied. Mathematically, the law is: F=ma or F = m(v-u)/t
- The Law of Action-Reaction (Third Law): To every action, there is an equal and opposite reaction.
Inertia and Mass – Inertia is the resistance of an object to changes in motion and depends on mass. Heavier objects have more inertia. i.e. A train resists motion more than a cart
Newton deduced that if Earth can attract an apple, it can also attract the moon. This led to the idea of centripetal force, which keeps objects moving in a circular path.
Universal Law of Gravitation states that every object in the universe attracts every other object with a force that is: The formula is F = G (M × m) / d2, Where, F = gravitational force, G = universal gravitational constant, M, 𝑚 = masses of two objects, d = distance between the centers of the two objects
- Directly proportional to the product of their masses.
- Inversely proportional to the square of the distance between them.
Acceleration due to gravity (g) is caused by the gravitational force exerted by Earth. It is a constant near the Earth’s surface, approximately 9.8 m/s², and is calculated using the formula: g=GM/r²where G is the gravitational constant, M is Earth’s mass, and R is Earth’s radius)
- According to Newton’s Second Law, the gravitational force F on a mass m is:
- Weight is the force of attraction by gravity and depends on the location. W=mg
- On the Moon, gravity is weaker. An object’s weight is 1/6th of its weight on Earth.
Mass and Weight – Mass is a measure of the amount of matter in an object, whereas weight is the force with which an object is attracted toward the Earth due to gravity.
Thrust and Pressure – thrust (force applied perpendicular to a surface) and pressure (thrust per unit area), A smaller area experiences greater pressure for the same force. The unit of pressure is Pascal (Pa).
Buoyancy and Archimedes’ Principle
when an object is immersed in water, it experiences an upward force called the buoyant force. Whether an object sinks or floats depends on the balance between this buoyant force and its weight. If the weight is greater than the buoyant force, it sinks (like an iron nail); if lesser, it floats (like a plastic bottle or cork). The principle of buoyancy was discovered by Archimedes.
Archimedes’ Principle is introduced, which states that a body fully or partially immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by it.
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