Transcript Momentum and Energy

Momentum and Energy
Chapter 9, 10, 11
Physics Principles and Problems
Zitzewitz, Elliot, Haase, Harper, Herzog,
Nelson, Nelson, Schuler and Zorn
McGraw Hill, 2005
The momentum of an object is the product
of that object’s mass and velocity.
p=m•v
http://kommandobryggan.se/ok/okbilder/oktavius2.jpg
http://www.digicamhistory.com/HaroldEdgertonBulletSmall.jpg
Therefore a large oil tanker (big m, small v) and moving
bullet (small m, big v) could have equal momentums.
An impulse changes an object’s momentum. It
is the product of force on an object and the
amount of time that force is applied.
F • ∆t = m • ∆v
http://discovermagazine.com/2008/the-body/11-turn-your-fistinto-a-blocking-breaking-machine/karate.jpg
http://sol.sci.uop.edu/~jfalward/physics17/chapter3/boxingglove.jpg
• The same impulse can be delivered in 2 ways:
Increasing the force that is applied or increasing
the time the force is applied.
Impulse - Momentum Theorem
F • ∆t = pf - pi
or
F • ∆t = mvf - mvi
• A 2200-kg car traveling at 26-m/s can be stopped in 21-s by
applying the brakes or in 0.22-s by hitting a wall. What is the
force exerted on the car in both of these situations?
pf = 2200-kg • 0-m/s = 0
F = pf - pi
∆t
pi = 2200-kg • 26-m/s = 57000-kg •m/s
0 - 57000 = -2700N OR 0 - 57000 = -260000N
21
0.22
Conservation of Momentum
• Within any
closed (no
change in mass),
isolated (external
forces are zero)
system the
momentum is
conserved or
does not change.
http://webpages.uah.edu/~wilderd/momentum.jpg
Elastic Collisions - Objects hit and bounce off
m1v1 + m2v2 = m1v3 + m2v4
where v1 and v2 are the velocities of the
objects before the collision and v3 and v4
new velocities after the collision. Notice
the masses haven’t changed.
http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0002/8ball.gif
Inelastic Collisions - Objects hit and stick
m1v1 + m2v2 = (m1 + m2)v3
where v1 and v2 are the velocities of the
objects before the collision and v3 is the new
velocities of the combined masses.
http://sol.sci.uop.edu/~jfalward/physics17/chapter3/trains.jpg
Energy, Work and Power
• Energy - the property or ability of an object to produce a
change in itself or the world around it.
• Work - a product of the force exerted on an object in the
direction of motion and the object’s displacement. W = F • d
(unit is the joule = N•m)
• Kinetic Energy - energy resulting from motion. KE = 1/2mv2
• Work-Energy Theorem - work is equal to the change in
kinetic energy. W = ∆KE
• Work with Angle - a product of the force and the
displacement, times the cosine of the angle between the
force and the direction of displacement. W = Fdcos
• Power - work done divided by the time taken to do the work.
P = W / t (unit is the watt = J/s)
Work and Power Problems
• The third floor of a house is 8-m above street level. How
much work is needed to move a 150-kg refrigerator to the
third floor?
• During a tug-of-war, team A does 2.2 x 105-J of work in
pulling team B 8-m. What force did team A exert?
• A wagon is pulled by a force of 38-N exerted on the handle
at an angle of 42° with the horizontal. If the wagon is pulled
in a circle of radius 25-m, how much work is done?
• A lawn mower is pushed across a lawn by a force of 155-N
along the direction of the handle, which is 22.5° above the
horizontal. If 64.6-W of power is developed for 90-s, what
distance is the mover pushed?