unit 2: mechanics

how is acceleration defined? what does this mean?

how is acceleration defined? what does this mean?

• acceleration is a change in velocity

• acceleration occurs whenever an object changes motion

• as velocity is a vector, acceleration occurs when an object changes direction

how do average and instantaneous speed differ?

• average speed = total distance / total time

• instantaneous speed is how fast an object is moving at a particular point in time

• generally we talk about average speed not instantaneous speed

using frames of reference to understand relative velocity

• the velocity of an object in relation to another object or observer

• by choosing a specific frame, we can measure the velocity of one object with respect to another

• from a car moving at 50 km/h the relative velocity of a car moving 60 km/h is +10km/h

Displacement-Time Graphs

The y-axis represents displacement, while the x-axis represents time. The slope of the graph indicates the object's velocity. A flat line represents zero velocity, a positive slope indicates constant forward motion, and a negative slope indicates constant backward motion.

velocity-time graphs

Graph that shows how an object's velocity changes over time. Steeper slope = acceleration. Flat line = constant speed. Negative slope = moving backwards. Area under the curve represents displacement.

acceleration-time graphs

The slope of the graph indicates the object's acceleration. A steeper slope represents a higher acceleration, while a flatter slope indicates a lower acceleration. The area under the graph represents the object's change in velocity.

terminal velocity

• maximum velocity that an object can reach when falling through a fluid

• occurs when the force of gravity pulling the object downward is balanced by the drag force exerted by the fluid

• at terminal velocity, the object no longer accelerates and falls at a constant speed

• the value of terminal velocity depends on the object's mass, shape, and the density of the fluid it is falling through.

acceleration of a falling object

• called free-fall when the effects of air resistance are ignored

• all objects in free-fall have the same acceleration independent of their mass

• this is acceleration due to gravity, it can be defined as positive or negative depending on whether up or down is defined as positive

horizontal and vertical components of projectile motion

• horizontal motion is unaffected by gravity and remains constant

• vertical motion is affected by gravity, following a parabolic path. It accelerates upwards until reaching maximum height, then accelerates downwards again

projectile motion

• projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity

• the only force acting on the object is gravity

impact of fluid resistance on parabolic motion

the magnitude of the drag force depends on…

• the relative velocities of the object and fluid

• the object’s shape + size (whether it is aerodynamic)

• the viscosity of the fluid

with fluid resistance a projectile following a parabolic path…

• does not goes as high

• does not go as far

• follows an asymmetrical path — the gradient is steeper when the projectile moves downwards

force

the cause of a deformation or change in velocity

a force…

• has a magnitude

• has a direction

• acts on an object

• is exerted by an object

free body diagrams

• used to show forces

• a longer arrow corresponds with a larger force

• the direction of an arrow is the direction of the force

• arrows should be labelled with the type of force

Newton's first law

An object at rest stays at rest, and an object in motion stays in motion with the same speed and direction, unless acted upon by an external force.

• a resultant force causes acceleration

• when the net force is zero the object is in equilibrium

Newton's second law

• the resultant force of an object is proportional to the rate of change of momentum

• using SI units: the resultant force is equal to the rate of change of momentum

Newton’s third law

• for every action by one object there is an equal but opposite reaction by another object

• the forces must be the same type

• the objects will accelerate differently when they have different masses

the difference between mass and weight

• mass refers to the amount of matter in an object, measured in kilograms (kg), and remains constant regardless of the object's location

• weight, on the other hand, is the force exerted by an object due to gravity, measured in newtons (N), and can vary based on the strength of the gravitational field

friction and types of friction

• friction = the force that opposes the relative motion of two surfaces

• static friction = both objects are at rest

• dynamic/kinetic friction = at least one of the surfaces is moving

coefficient of friction

• the maximum frictional force and normal force are proportion

• the coefficient of of friction is the ratio between the friction and normal forces

• it is less than 1 unless the surfaces are stuck together

when is work done?

• when a force moves its point of application to the direction of the force

• the force and displacement are in the same direction

• the area under the curve on a force-displacement graph

conservation of energy

• energy cannot be created or destroyed, only transferred or transformed from one form to another

• total energy contained within a system is constant

link between energy and work

• the amount of energy transferred is equal to the amount of work done

• energy is a measure of the amount of work done

power

• the rate at which energy is transferred

• if an object is moving at a constant velocity against a frictional force the power it needs is P=Fv

efficiency

• energy transferred can be considered useful or not useful

• ratio of useful energy to total energy

• equal to the useful work/energy/power OUT / total work/energy/power IN

linear momentum

• product of mass and velcoity

• always a vector

impulse

change in the momentum of an object

conservation of momentum

provided there is no external force the total linear momentum of a system of interacting particles remains constant

elastic collision

• no mechanical energy is lost

• momentum is conserved

• an object of velocity v collides with an object at rest, the first object becomes at rest and the second moves at exactly v

• does not happen in reality

inelastic collision

• some mechanical energy is lost

• momentum is conserved

• both objects have a new velocity after colliding but are not stuck together

totally inelastic collision

• momentum is conserved

• a large amount of mechanical energy is lost

• the objects stick together so their relative velocity of separation is zero