Kinematics 1D
Kinematics 2D
Dynamics
Work and Energy
Kinematics – 1 Dimension
All about motion problems
Frame of Reference – orientation of an object’s motion
Used to anchor coordinate axes
For many problems, you can choose the orientation of your coordinate axes (down is positive and up is negative, if you like)
Be logical though! Don’t try to complicate the problem more than it is already.
Kinematics – 1 Dimension
Kinematics – 1 Dimension
Some vocab
Scalar
Vector
Distance
Displacement
Average speed
Average velocity
Instantaneous velocity
Acceleration
Average acceleration
Instantaneous acceleration
Kinematics – 1 Dimension
Motion at Constant Acceleration
Use your Kinematic Friends!
Most, if not all, kinematic problems are constant acceleration problems
Falling Objects
Uniform acceleration of 9.81 m/s2
The sign of g depends on your frame of reference
Kinematics – 1 Dimension
PT Graphs
Slope = velocity
+ slope = + velocity
- slope = - velocity
0 slope = 0 velocity
VT Graphs Slope = acceleration + slope = + accel.
- slope = - accel.
0 slope = 0 accel.
Curve sloping toward x-axis = slowing down
Curve sloping away from x-axis = speeding up
Kinematics – 1 Dimension
Multiple Choice Questions – TIMED!
Quietly answer the questions on your own.
Multiple Choice Answers
1. D
2. D
3. A
4. E
5. B
6. C
7. D
8. A
9. E
10. B
Kinematics – 2 Dimensions
Vector Addition – Graphical Method Head – to – Tail Method Place the head of the first vector at the tail of the second
vector
Repeat for successive vectors
For the resultant vector, draw an arrow from where you started to where you ended (from tail of first vector to head of second vector).
Use ruler to measure length (magnitude)
Use protractor to measure direction w.r.t. a reference axis
Kinematics – 2 Dimensions
Vector Addition – Mathematics Method
Adding by components
Breaking a vector down into components is called vector resolution
Add x-components together to get Rx
Add y-components together to get Ry
Pythagorean theorem, sqrt(Rx2 + Ry
2)
tan-1 = (opp. component/adj. component)
Kinematics – 2 Dimensions
Vector Addition
To subtract a vector, flip the direction by 180˚
Multiplying a vector V by a scalar, c, produces a vector with magnitude cV in the direction of V.
Kinematics – 2 Dimensions
Projectile Motion Vertical component of motion is independent of
horizontal motion Horizontal component is constant (vix = vfx and ax = 0)
Vertical component changes with g
How to solve Treat motions separately!
Write displacement, velocity and acceleration in terms of x- and y-components. USE KINEMATIC FRIENDS!
Use t-chart method or some other strategy to organize data
Kinematics – 2 Dimensions
Projectile Motion, con’t
The only data common to both motions is the time of flight (t) and the angle of launch (θ)
Often you will need to solve a systems of equations
Because time and the angle are constant to both motions, solve one equation for time or angle and substitute
Kinematics – 2 Dimensions
Relative Motion
Problems are simply vector addition problems
Kinematics – 2 Dimensions
Kinematic – 2 Dimensions
Multiple Choice Questions – TIMED!
Quietly answer the questions on your own.
Multiple Choice Answers
1. D
2. C
3. E
4. B
5. C
6. A
7. C
8. E
9. D
10. B
Dynamics: Motion and Force
Force is a push or pull between two objects
Vector! Magnitude and direction
Newton’s First Law of Motion (Law of Inertia)
An object in motion will stay in motion, and an object at rest will stay at rest, unless acted upon by an unbalanced force
Inertia – ability of an object to maintain motion (resistance to change in motion)
Depends on mass of object (more mass = more inertia)
Dynamics
Mass is the measure of ‘amount of stuff’ – measured
in kilograms
Weight is the measure of ‘the force of gravity on that stuff’ – measured in Newtons
Newton’s Second Law of Motion
∑F = ma
Balanced forces, ∑F = 0
Unbalanced forces result in an acceleration of the object
Dynamics
How to solve problems
Draw a FBD!
Summation of forces
∑F = max
∑F = may
Apply Kinematic Friends as needed
Dynamics
Newton’s Third Law of Motion
For every action there is an equal and opposite reaction
Forces come in pairs – there must be two objects for forces to exist
Dynamics
Other Forces
Normal force – force due to the contact between an object and a surface
Frictional force – force between two surfaces sliding (kinetic), or trying to slide (static), across each other – dependent on normal force
Spring/Elastic force – restoring force due to a spring or other elastic object
Tension – force due to rope, string, cord, wire, etc.
Dynamics
Dynamics
Multiple Choice Questions – TIMED!
Quietly answer the questions on your own.
Multiple Choice Answers
1. B
2. D
3. A
4. D
5. C
6. E
7. B
8. D
9. D
10. C
Work and Energy
Work Done By a Constant Force
W = Fdcosθ
θ is the angle btn force and displacement
Work is measured in Joules
The perpendicular component of the force does no work
Work done by friction is always negative since it opposes motion
Work and Energy
Work Done By a Varying Force
Use a force-displacement graph
Find the area under the curve
Work and Energy
Conservation of Energy
Energy cannot be created nor destroyed
Kinetic Energy KE = ½ mv2
Energy due to an object’s motion – has the capacity to do work
Work-Energy Theorem
The work done on an object will result in a change in its kinetic energy and, subsequently, a negative change in its potential energy W = ΔKE and W = -ΔPE
Work and Energy
Potential Energy
Due to its position with regard to other bodies
Gravitational potential
Refers to capacity of an object to do work based on the force of gravity acting on it
PEg = mgh, h is determined by your zero level
Spring/Elastic potential
A spring stretched or compressed has the capacity to do work once that displacing force is removed
PEs = ½ kx2
Work and Energy
Conservative Forces
Forces for which the work done is independent of the path taken
Work depends only on starting and finishing positions
Examples: gravity, spring/elastic, etc.
Non-Conservative Forces
Work done depends on path taken
Example: friction
WNC = ΔKE + ΔPE
Work and Energy
Power
Rate at which work is done
OR
Rate at which energy is transformed
P = W/t OR P=E/t
Measured in Watts, W
Work and Energy
Work and Energy
Multiple Choice Questions – TIMED!
Quietly answer the questions on your own.
Multiple Choice Answers
1. E
2. D
3. B
4. E
5. D
6. E
7. C
8. B
9. A
10. E