module 3

• Equation of motion for a particle moving with uniform acceleration in one dimension:

  • s = ut + 1/2 at^2
  • s = distance travelled by the particle
  • u = initial velocity of the particle
  • t = time taken by the particle to travel the distance s
  • a = acceleration of the particle

  
• Projectile motion:

  • A projectile is an object thrown at an angle to the horizontal, moving in both horizontal and vertical planes
  • Initial vertical velocity = v sin α, initial horizontal velocity = v cos α
  • Horizontal velocity remains constant throughout the motion, while vertical velocity changes due to acceleration of free fall, g

  
• Speed is defined as the rate of change of distance, with the equation v = Δx/Δt and SI unit ms^-1
• Instantaneous speed is the speed of an object over a very short time interval, determined by analyzing the gradient of a distance-time graph at a given time
• Displacement is the distance an object has traveled in a given direction, a vector quantity with both magnitude and direction
• Velocity is the rate of change of displacement, given by the formula v = Δs/Δt in ms^-1
• Acceleration is the rate of change of velocity, expressed as a = Δv/Δt, a vector quantity indicating speed increase, decrease, or change in direction
• Graphical representations of speed and velocity show a flat line for a stationary object, a constant gradient for constant velocity, and a curved line for accelerating or decelerating objects
• The area under a velocity-time graph represents the displacement of the object, with a linear graph allowing mathematical calculation and a curved graph requiring estimation techniques
• Four equations of linear motion for an object with constant acceleration:

  • v = u + at
  • s = ut + 1/2 at^2
  • v^2 = u^2 + 2as
  • s = 1/2 (v+u)t
• Stopping distances of a car consist of thinking distance (proportional to initial speed and reaction time) and braking distance (proportional to the square of initial speed)
• When a resultant force, F, acts on a body with mass m, the body will accelerate
• Resultant force is related to mass and acceleration by the formula F = ma, with the SI unit for force being kgms-2 or the commonly used Newton, N
• Weight of an object is the gravitational force acting upon it, determined by the formula F = mg where g is the acceleration due to gravity
• Commonly occurring forces include weight, friction, drag, tension, up-thrust, and normal contact force
• Free body diagrams model all forces acting on an object, with each force represented as a vector arrow scaled to its magnitude and direction
• Motion under constant force results in a net acceleration, determined by F = ma, and can be extended to a 2-D plane like a slope
• Drag force opposes motion in a fluid, with magnitude depending on factors like speed, object's shape, and fluid density
• Terminal velocity is reached when drag force equals the weight of an object, resulting in zero net force and no further acceleration
• Terminal velocity can be experimentally determined by observing a ball bearing in a viscous fluid, marking its position at regular time intervals
• Equilibrium is achieved when the sum of all forces and moments acting on an object is zero
• Moment of a force is the turning effect measured in Nm, calculated as the magnitude of the force multiplied by the perpendicular distance from the force to the pivot
• Moment of a force is defined as the magnitude of the force multiplied by the perpendicular distance from the force to the pivot, measured in Nm
• If a force is not acting perpendicular to the pivot, it may be necessary to resolve the force or the distance to find the perpendicular component
• A couple is a pair of forces with equal magnitude and opposite direction, applied to a body in parallel with each other and along different lines, producing a rotational force about the central pivot point with no translational movement
• The torque of a couple is the product of the magnitude of one of the forces and the perpendicular separation between the forces, equal to the total moment of the couple
• In equilibrium, the net force acting on a body is 0, and its net moment is also 0, known as the principle of moments
• The principle of moments states that for a body in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anti-clockwise moments about the same point
• The centre of mass of an object is the point where the entire weight of the object appears to act, and it is the point through which the application of an external force produces only motion in a straight line, with no rotation
• An object will come to rest with its centre of mass vertically below its suspension point, allowing a plumb line to be used to determine the centre of mass
• Density of a substance is defined as the mass per unit volume, measured in kgm-3, and can be determined using different methods depending on the object
• Pressure is the normal force exerted on a surface per unit cross-sectional area, measured in Nm-2 (Pascal)
• Archimedes' principle states that the upthrust exerted on a body immersed in fluid is equal to the weight of the fluid that the body displaces
• Work done is the transfer of energy when a force is required to provide motion, defined as the product of the force's magnitude and the distance moved by the object in the direction of the force
• The unit for work done is joules, with 1 joule being the work done when a force of 1 N moves an object 1m in the direction of the force
• The principle of conservation of energy states that in a closed system, energy cannot be created or destroyed, only transferred between different forms
• Forms of energy include kinetic, gravitational potential, elastic potential, electric potential, sound, internal, electromagnetic, nuclear, and chemical energy
• Kinetic energy is associated with an object's motion, measured in joules, and can be calculated using the formula 1/2 * m * v^2
• Gravitational potential energy is an object's capacity to do work due to its position in a gravitational field, gained when moving higher against gravity and lost when falling back down
• The velocity of an object at a given position in a gravitational field can be calculated using the formula v = √(2gh)