Download Momentum and Energy

The momentum of an object is the product of
that object’s mass and velocity.
p=m•v
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
The same impulse can be delivered in 2 ways:
• Increasing the force that is applied.
• 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
21
OR
0 - 57000 = -260000N
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.
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.
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.
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.
• Kinetic Energy - energy resulting from motion.
• Work-Energy Theorem - work is equal to the change in kinetic
energy.
• Power - work done divided by the time taken to do the work.
Work and Power Problems
1. 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?
1. 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?
1. 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?
1. 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?