forces
1.5.1 | effects of forces
changes in size and shape
forces can cause compression, extension, deformation, or permanent changes to objects.
load–extension graphs
attach object vertically, add equal load increments, measure length changes, plot load vs extension. linear region obeys hooke's law; beyond the limit of proportionality, the relationship becomes non-linear.
resultant force
vector sum of multiple forces along the same line. f_resultant = f₁ + f₂ + f₃. when zero, object is in equilibrium.
newton's first law
object remains at rest or moves at constant velocity unless acted on by a resultant force.
changes in velocity
resultant force changes velocity by:
- changing direction (perpendicular force)
- changing speed (parallel force)
spring constant
k = f/x (unit N/m). hooke's law: f = kx within the limit of proportionality, where material stops obeying hooke's law. the limit of proportionality is shown by the point where the load-extension graph stops being a line, and curves away.
newton's second law
f = ma, where m is mass of object and a is acceleration of object. force and acceleration are in the same direction.
circular motion due to perpendicular force
- speed increases if force increases (constant mass and radius)
- radius decreases if force increases (constant mass and speed)
- increased mass requires increased force (constant speed and radius)
friction
solid friction: opposes motion between surfaces, causes heating.
liquid drag: opposes motion through liquids, increases with speed and viscosity.
air resistance: opposes motion through air, proportional to v².
1.5.2 | turning effect of forces
moment of a force
measure of a force's turning effect about a pivot.
moment definition
m = f × d (unit: Nm), where d is perpendicular distance from pivot.
complex situations
calculate moment for each force separately, sum clockwise and anticlockwise moments, equate them for equilibrium.
experimental demonstration
hang mass on one side of meter rule pivot, balance with another mass, measure distances. verify: f₁ × d₁ = f₂ × d₂.
you can use moments to find mass! mark centre of mass, find the distance from the pivot to the centre of mass, then find the moments on the object. the missing moment value divided by the distance from the centre of mass to the pivot will be the weight of the object, which after dividing by 9.8, will be the mass!
centre of gravity
the point where the entire weight of an object acts. for uniformly-shaped objects, it is at the geometric centre.
1.5.3 | centre of gravity
the single point where the the entire weight of an object acts is the centre of gravity.
finding centre of gravity of an irregular shape
hang the shape from different points near its edge. hang a plumb line from the same point and draw a vertical line on the shape. repeat from multiple holes. the centre of gravity is where the lines intersect.
effect of position of centre of gravity on stability
- lower centre of gravity = more stable
- higher centre of gravity = less stable
- wider base = more stable
- narrow base = less stable
- line of action of weight must fall within base for stability
the line of action is a straight, imaginary vertical line through the centre of gravity.