Kinematics 1D Kinematics 2D Dynamics Work and Energy
Kinematics 1 Dimension
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 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/s 2 The sign of g depends on your frame of reference
PT Graphs Slope = velocity Kinematics 1 + slope = + velocity - slope = - velocity 0 slope = 0 velocity Dimension 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
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 R x Add y-components together to get R y Pythagorean theorem, sqrt(r x 2 + R y2 ) tan -1 = (opp. component/adj. component)
Vector Addition Kinematics 2 Dimensions 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 (v ix = v fx and a x = 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
Relative Motion Kinematics 2 Dimensions Problems are simply vector addition problems
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
Dynamics 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)
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 Dynamics Unbalanced forces result in an acceleration of the object
How to solve problems Draw a FBD! Summation of forces F = ma x Dynamics F = ma y 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
Other Forces Dynamics 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 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 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 mv 2 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 PE g = 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 PE s = ½ kx 2
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 W NC = ΔKE + ΔPE
Power Work and Energy 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 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