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Momentum and Energy
PHYS 1090 Unit 3
Question
If a car collides with a bug, which
experiences the greatest force?
A.
B.
C.
D.
The car.
The bug.
It’s a tie.
Insufficient information to answer.
Force Meters
Newton’s Third Law
• Whenever one object exerts a force on a second
object, the second object exerts an equal and
opposite force on the first, along the same line of
interaction.
• To every action there is always an opposed
equal reaction.
• If object A exerts force F on object B, object B
exerts force –F on object A.
FA→B = −FB→A
Bug + Windshield
Small car: 1250 kg
Large insect: 0.00025 kg
From the same force, the
bug accelerates a lot more!
Forces are the same—the accelerations
are different.
Interaction Forces
All forces are interaction forces!
– gravity
– wind
– jumping
– everything!
• This means: whenever something
accelerates, something else accelerates in
the opposite direction! Whoa!
Pulleys
Pulleys
• Change the direction but not magnitude of
the tension in the cable
• Lift force is tension
times number of
segments lifting
• Lift height is pull divided
by number of segments
Levers
Levers
• To balance a load, the force closest to the
fulcrum must be larger
Levers
• To balance a load, the force closest to the
fulcrum must be larger
• The load farthest from the fulcrum moves
the most
Inclined Planes
Inclined Planes
• The steeper the plane, the greater the
force required
• The steeper the plane, the shorter the
distance pulled to reach the same height
Simple Machines
• All are a trade-off between force and
distance (or force and speed)
• The greater force moves the least distance
F1Dd1 = F2Dd2
Work
Formula
work = F·Dd
F = force applied
Dd = distance traveled
Simple Machines
F1Dd1 = F2Dd2
Work input = Work output
• Forces are different
• Distances are different
• Work is the same.
Work and Energy
• Doing work on something changes its
energy.
• Energy: “the ability to do work”
Conservation of Energy
• Energy can be transferred between
objects or transformed into different forms,
but the total amount of energy can never
change.
Rail Cart Collisions
Rail Cart Collisions
• Accelerations are in opposite directions
• More massive cart accelerates the least
• Equal-mass carts have equal
accelerations (in opposite directions)
• Total Mass·Velocity the same before and
after collisions
Air Hockey Collisions
Air Hockey Collisions
• Accelerations are in opposite directions
• More massive disk accelerates the least
Momentum
•
•
•
•
•
“Inertia in motion”
Massive objects are hard to get going.
Massive objects are hard to stop.
It is hard to give an object a high speed.
It is hard to stop a high-speed object.
Momentum
Formula
p = mv
momentum is a vector.
Momentum Changes and
Newton’s Third Law
• At any instant:
Dp = D(mv) = mDv = maDt = m(F/m)Dt = FDt
• For interacting objects, FA = −FB, so:
DpA = FADt
DpB = FBDt = −FADt
DpA = − DpB
Conservation of Momentum
• Momentum can be transferred between
objects, but the total momentum can never
change.
Dp1 + Dp2 = 0
Rollerballs and Drag Meters
Rollerballs and Drag Meters
• The lighter the meter, the farther it drags.
• The heavier the ball, the farther it drags a meter.
• The higher the ramp, the farther a ball drags a
meter.
• The higher the ramp, the faster a ball rolls at the
bottom.
• The mass of the ball has no influence on how
fast it rolls at the bottom.
Some Forms of Energy
• Potential Energy
• Kinetic energy
Work Against Gravity
Force = –w = mg
distance = h
work = mgh
Source: Griffith, The Physics of Everyday
Phenomena
Get It Back?
Gravity exerts force
mg as object drops
distance h.
work = mgh
Source: Griffith, The Physics of Everyday
Phenomena
Potential Energy
The energy of relative position of two objects
gravity
springs
electric charges
chemical bonds
Potential Energy
Gravitational potential energy =
the work done by gravity in lowering an object
– or –
the work to raise an object to a height
Gravitational PE = mgh
A Moving Object Can Do Work
Source: Griffith, The Physics of Everyday Phenomena
Kinetic Energy
the work that a moving object does in
stopping
– or –
the work to bring a motionless object to
speed
KE =
1
2
mv2
Rollerball Energy Conversions
Potential energy
work
Kinetic energy
work
The more work you put in, the more work
you get out!