Physics 1A Lecture 8A
Review of Last Lecture A closed system is one which does not exchange (mechanical) energy with its environment total mechanical energy is conserved in this system Force is the negative derivative of potential energy with position (F = -du/dx) Energy diagrams (potential energy versus position) allow one to visualize balance of potential and kinetic energy and constrains motion If dissipative forces are present and energy transferred, E final = E initial W nc E transfer
Not all forces do work equally N MOTION F f Mg forces orthogonal to motion do no work normal forces never do work these are constraint forces Examples: normal force, tension in pendulum, gravity in perfectly circular orbit
Perfect Circular motion Δx F grav Force vector is always perpendicular to displacement => no change in kinetic energy or speed
Using Energy & Newton s Laws together You now know two approaches to solving kinetic problems: Newton s Laws: a = F/m Energy: ΔE = Δ(K + U) = W nc Which one you use or both will depend on what you know and what you want to know. In general: motion over time => Newton motion in space => Energy closed system => Energy or Newton constant force => Energy or Newton space-dependent force => Energy
Rest of today s lecture Momentum Momentum conservation in isolated systems Impulse Momentum & Energy conservation problems
Kinematic quantities to date : position, velocity and acceleration - vector quantities magnitude and direction - measurable : kinetic energy - scalar quantity magnitude only - not directly measurable
Linear Momentum Vector quantity: magnitude & direction Dimensions: [p] = M L T -1 SI Units: kg m/s First suggested by Abu Ali Ibn Sina: mayl = weight x velocity Abu Ali Ibn Sina (AD 980-1037)
From Principia:
Momentum & Newton s Laws doesn t change definition of acceleration
Conservation of Linear Momentum Consider a system of two interacting particles Newton s 3rd Law: Linear momentum of an isolated system is conserved
Newton s 2 nd law is a vector equation y axis etc... x axis change in momentum is always in the same direction as applied force
Baseball vs. Bowling What s the more exciting sport? (from a Physics perspective)
Estimates in SI units (kg m s): mass (kg) velocity (m/s) momentum (kg m/s) K (kg m 2 /s 2 ) Fast pitch baseball 0.1 50 5 125 Bowling ball 5 10 50 250 Hints: 1 mph 0.5 m/s, 1 lb 0.5 kg
Baseball vs. Bowling What s the more exciting sport? (from a Physics perspective)
Impulse Newton s Second Law: Impulse Dimensions: (M L T -2 )(T) = M L T -1
Impulse Newton s Second Law: Impulse-Momentum Theorem The impulse of the net force on a particle equals the change in momentum Impulse Dimensions: (M L T -2 )(T) = M L T -1 Vector quantity
Impulse: Area under the curve Force (N) along one axis measures the area under a force curve versus time Time (s) If you know how force changes with time, you can calculate change in momentum = change in momentum along one axis
Work: Area under the curve Force (N) along one axis measures the area under a force curve versus space Position (m) If you know how force changes with distance, you can calculate change in kinetic energy = change in kinetic energy (work)
Energy and Momentum: A Comparison Energy/Work Momentum/Impulse Definitions: Relation to Forces: Force over distance Force over time
For Next Time (FNT) Start reading Chapter 8 Start homework for Chapter 8