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FY S I CAHoorcollege februari
MOTION (KINEMATICS) in one and multiple dimensions
Mechanics focusses on describing the (i) motion of objects and (ii) forces that cause this motion to
change. Divided in:
Kinematics: describes how objects move without any reference to what is causing motion.
- Variables:
- Time (seconds)
- Position (meters)
- An object’s position is its location with respect to a chosen reference point.
- Displacements & distance (meters)
- Displacement is de ned as the change in position of an object, i.e., how far is it from the starting
point?
- Represented as delta X, where delta X = X nal - X initial
- Has a magnitude & direction (it is a vector)
- Example: meters ‘east’
- Velocity & speed (meters/seconds)
- Average velocity is de ned as the displacement divide by the time taken to displace.
- Average speed is de ned as the total distance travelled divided by the time taken to travel this
distance.
- CRUCIAL DIFFERENCE: velocity is vector quantity, speed is a scalar quantity
- The average speed is not necessarily equal to the magnitude of the average velocity.
- The instantaneous velocity is de ned as the average velocity over an in nitesimally short time
period, i.e., delta T —>
- The instantaneous velocity is the slope of the tangent to the postion-time graph at some instant
- Acceleration (meters/seconds^ )
- The average acceleration is de ned as the change in velocity divided by the elapsed time.
- The instantaneous acceleration is the limiting value of the average acceleration as delta T —>
- The slope in a velocity-time graph gives the acceleration.
Acceleration & velocity
- When an object’s velocity and acceleration are in the same direction, the object is speeding up.
- When an object’s velocity and acceleration are in the opposite direction, the object is slowing down.
- Negative acceleration does not mean the object is slowing down, the object could in fact be speeding up!
- If you were given the acceleration as a function of time, how do you calculate the postion as a function of
time?
- You need to work backwards and integrate!
Dynamics: deals with things that cause acceleration: forces!!
Motion at constant acceleration |SLIDE |
Graivty points in oppositie direction to
increasing y - true for most examples.
1 5 1 fifi fi70 fi2 fi fi20 fi 0
, General motion & VECTORS
In two/three dimensional kinematics, we need to use vector notation to describe motion.
Scalars: A scalar quantity is speci ed by a single value & has no direction. (Time, distance, mass, speed)
Vectors: a vector quantity is speci ed by a number & a direction (displacement, velocity, acceleration)
- suppose a particle travles from A to B along the path shown by the broken line. The distance travelled is
the length of the broken Line is a scalar. The displacement is the solid line from A to B and is a vector.
- Notation: a vector is represented by bold text with an arrow, the magnitude is represented by absolute
stripes.
- Magnitude has physical units and is always a positive number.
- never confuse vectors and scalars!! You must put an arrow over vectors
- Two vectors are equal, if they have the same magnitude & they point in the same direction.
- The resultant (sum of two vectors) is drawn from the origin of the rst vector to the end of the last vector
- De ned as the vector that, when added to the original vector, gives a resultant of .
- Same magnitude as original but opposite direction: ‘-A’
- Multiplying or dividing a vector by a scalar yields a vector.
- If the scalar is postive/negative, the resultant vector is in the same/opposite direction as the original
vector.
- Key: components of a vector
- A component is a projection of a vector along an axis. Any vector can be completely described by its
components.
- Magnitude = pythagoras
- Key: unit vectors
- A unit vector is a dimensionless vector of magnitude of . The are used to speci c direction & have no
other physical signi cance.
- The symbols I,j, k represent unit vector point along the x,y,x.
- Wel met hoedje want dat is a unit vector!
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, Hoorcollege februari
NEWTON’S LAWS and their application to friction & circular motion
Force: a thing that cause an object’s velocity to change.
- Contact forces: involves physical contact between two objects, e.g, kicking a football
- Field forces: forces act through empty space (no physical contact)
- Vector quantities
- Have magnitude & direction
- The net total force is the sum of vertical and horizontal forces.
- It doesn’t take a force to keep an object moving in a straight line, it takes a force to change its motion.
- The force of friction causes the book to stop moving
FIRST LAW: law of inertia states that
‘Every object continues in its state of rest, or of uniform velocity in a straight lines, as long as not net force acts on it.’
Inertia: the tendency of an object to maintain its state of rest or uniform velocity in a straight line.
- An inertial reference frame is a reference frame where Newton rst law is valid. Not valid in rotating or accelerating
frames!!
- Suppose your reference frame is in an accelerating car. A cup on the dashboard suddenly move towards you even
though no force was exerted.
- Newton’s rst law does not hold in an accelerating reference frame!! This is a ‘non-inertial’ reference frame.
MASS
A measure of the inertia of an object; the more mass an object has, the greater the force needed tot accelerate it.
- independent of an object’s surroundings
- Independent of the method used to measure it.
- Is scalar quantity
- No direction
- SI units are the kilogram ‘kg’
- Mass and weight are two different quantities!!
- Weight: the magnitude of the gravitational force exerted on an object and thus varies with location (unlike mass)
SECOND LAW
When viewed form an inertial reference frame, the acceleration of an object is:
. Directly proportional to the net force acting on it &
. Inversely proportional to its mass (onder de streep kleiner, heel het getal groter)
Vector sum of all forces acting on the object
Force is the cause of changes in motion. Recall from before:
‘A force is that which causes an acceleration’
SI unit: N i.e. kg m/s^
Questions: what average net force is required to bring a 1500 kg car to rest from a speed a 100 km/hr within a distance of 55 m?
The initial velocity= . m/s. The nale velocity = m/s
v^ = v ^ + a(x-x )
Net force required
F=Mxa
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