Force
- Anything that changes/tends to change the state of motion of an object
- Can cause acceleration (no acceleration, no force present)
- = mass x acceleration
- Vector (b/c acceleration is a vector), so can be represented using arrows, which signify two things: the magnitude of the force (length of the arrow) and the direction of the force (where the arrow points to)
NOTE: Objects can be taken as point particles (for illustration)
Mass
- Amount of matter in an object
- Never changes
- Unit: kg
- Scalar
- Can never be 0
- Intrinsic
- Measured using triple beam/digital balance/lever
Weight
- Force of gravity pulling on an object
- Changes if gravity changes
- Unit: N
- Vector
- Can be 0
- Extrinsic
- Measured using a spring/scale/spring scale
*Gravity is not acceleration due to gravity (which is what’s changing)
Converting between mass and weight
W = mg (weight = mass x acceleration due to gravity [we use W or mg to represent weight])
Same as F = ma
Tension (T)
- Pulling force on an object
- Involves rope/string/wire/cable (if you see these things, think tension)
*In ex., arrow towards person pulling b/c tension toward him (pulling toward him)
*In ex. 2, b/c the ceiling is the one holding it, it’s pulling
Normal reaction force (R)
- Force between two surfaces in contact
- Acts perpendicular to the surface (at surface/point of contact)
Gravitational force (W or mg)
- Force that pulls objects downwards
- Always acts downwards (and on every object)
*Normal force starts at point of contact (surface) and gravity starts at center
Friction force (F)
- Force that opposes motion
- Also at point of contact (MW)
Upthrust (U)
- Buoyancy
- Experienced by a body immersed in a fluid
- Pushes objects upwards
- Placement of arrows doesn’t matter
Air resistance (R)
Opposes motion of an object through the air
Free-body diagrams
A diagram that shows only the forces acting on a specific object (if there was a box and a table, the question would tell us what to focus on)
*On a ramp, weight bigger b/c it’s what’s pulling it down
*W/ the ceiling thing, tension, again, longer b/c the ball isn’t falling down (something’s holding it up)
*For object attached to two strings on the ceiling, one of the T’s would equal weight b/c they’re not on the same line of action (?)
NOTE
*if forces in the same line of action have to be 0, we may have to resolve certain forces (ex. If we find the vertical components, add them up, and they add up to net force = 0)
*Constant speed/velocity means no acceleration and, thus, no net force
*R could’ve been from the top, but to make it look nice, we connect them
*See examples (motion of parachutist, car moving to the right)
*See ex. (ff moving horizontally, vertical forces must be balanced [also, if accelerating force—?—was less than friction, car would be deccelerating/slowing down])
*Can have equilibrium in rota
*See elevator ex.
Addition of forces
Forces are vectors and must be added vectorially (length and direction must be considered):
- Opposite forces have opposite signs
- Equal parallel forces are the same
- Sum of forces is called resultant force
*Also, remember Pythagoras’s Theorem and to use the parallelogram/head-to-tail method for direction
Balanced forces
- Forces on an object are said to be balanced if the net force is 0
- For the net force to be 0, vertical forces must be equal (up = down) and horizontal forces must be equal (left = right)
*Remember that if resolving, horizontal components must equate as well
*Draw triangles, use trig, ex. W = sum of vertical component of R + vertical component of F
*See formulae, but calculate to make sure
*Tension was 0 in that first example b/c both falling at the same time
Hooke’s Law
- States that the extension of a spring is proportional to the force applied to it
- Once you remove a sign of proportionality, you need a constant so F = kx, and if F = kx, k = F/x (where k is the spring constant [unit: Nm-1])
- F/W/Load may be on y-axis (and x on x-axis) for slope ot be k
- If x is on y-axis (and F is on x-axis), slope is 1/k
*Doesn’t have to pass through origin (sometimes, systematic error)
*When the variables are flipped (axis-wise), the slope becomes the inverse of the original
Newton’s 1st Law
- States that an object will remain at rest or move at uniform velocity (maintain any state of motion) unless acted upon by an unbalanced [external] force
- As long as there’s no unbalanced force present, an object will mai (only an unbalanced net force makes an object accelerate)
- If net force is 0, acceleration is 0
- Fnet = ma (NET force, as there can be more than one force present)
Translational equilibrium
- An object is said to be in translational equilibrium if the net force is 0
- In other words, no acceleration
Conditions necessary for an object to be in equilibrium
- Object may be at rest
- Object may be moving at constant velocity
- Object’s net force must be 0
*You can’t say for sure that the object is either at rest or moving at constant velocity, but you can say for sure that the object’s net force is 0
