Transcript Chapter 11: Forces

Bellringer 10/25
• A 95 kg clock initially at rest on a
horizontal floor requires a 650 N horizontal
force to set it in motion. After the clock is
in motion, a horizontal force of 560 N
keeps it moving with a constant velocity.
Find µs and µk between the clock and the
floor.
Chapter 5: Work & Energy
The Work/Energy Relationship
• Work is the use of force to displace an
object in the direction of the force.
Work done by a constant net force:
W = F∆x
For forces applied at an angle, θ:
W=Fcosθ d
“d” is the magnitude of displacement
• If an object is not displaced when a
force is applied to it, then no work
has been done on that object.
 Work is only done when a force causes an
object to move some distance.
 Work is measured in units called Joules (J).
 Work is a scalar quantity that can be
positive or negative.
• Positive work results in a displacement in the same
direction as the applied force.
Fnet
Displacement
• Work is negative when the force is opposite the
displacement.
Friction is doing negative work on the box.
Fk
Fnet
Displacement
Work can be positive or
negative
• Man does positive work
lifting box
• Man does negative
work
lowering box
• Gravity does positive
work when box lowers
• Gravity does negative
work when box is raised
Example
• How much work is done on a vacuum
cleaner pulled 3.0m by a force of 50.0N at
an angle of 30 degrees above the
horizontal?
Example
• A student drags a physics teacher for 25
m on the end of a rope that makes a 40
degree angle with the ground. The force
on the rope is 650 N. How much work is
done?
• Frictional work is done whenever the
force of friction hinders motion.
 For instance, when pulling a sled over concrete, a
significant amount of friction prevents the sled
from being pulled as far.
Work done by friction:
Wf = FkΔx
• Applying force at an angle can alter the
frictional force.
Fy
Fy
Reduction of frictional force
because Fy is upward, and reduces
the normal force.
Increase of frictional force because
Fy is downward, and increases the
normal force.
• The net work done on an object can be expressed
as the change of the object’s kinetic energy.
• This expression is known as the “Work - Kinetic
Energy Theorem.”
• Kinetic Energy is the energy of an object
due to its motion.
Net Work Done on an Object/ Work-Kinetic Energy
Theorem:
Wnet = ∆KE = ½mv2 – ½mv02
Kinetic Energy of an Object:
KE = ½mv2
Example
• A 7.00 kg bowling ball moves at 3.00 m/s.
How fast must a 2.45 g table tennis ball
move in order to have the same kinetic
energy as the bowling ball? Is this speed
reasonable for a table tennis ball in play?
Example
• On a frozen pond, a person kicks a 10.0kg
sled, giving it an initial speed of 2.2 m/s.
How far does the sled move if the
coefficient of kinetic friction between the
sled and the ice is 0.10?
Bellringer 10/31
• Determine the amount of work that must
be done by the engine of a 500 kg racing
car to change the velocity of the car from
55 ms-1 east to 60 ms-1 east.
• If this change in velocity was
accomplished in 0.3 s, calculate the
acceleration of the car.
• Find the net force applied by the engine to
cause this acceleration
Review
• Work – only done on an object when a net
force acts to displace it (W=Fd)
• Energy
 Objects in motion have kinetic energy (KE =
1/2mv2)
 Net work done on or by an object is equal to
the change in kinetic energy of the object
(W=ΔKE)
Review
1. How much work is done in lifting a 300N
rock 10m off the ground?
2. Calculate the kinetic energy of a 3.1kg
toy cart that moves at 4.8m/s. Calculate
the kinetic energy of the same cart at
twice the speed.
3. A car is travelling at 27 m/s north and has
a mass of 1500 kg. Calculate the kinetic
energy of the car.
• Friction is an example of a nonconservative
force – one that randomly disperses the
energy of the objects on which it acts.
• For example, the car shown is
undergoing frictional
forces as it slides.
• The energy is being
dissipated as sound
waves and thermal
energy.
• Gravity is an example of a
conservative force. It does
not dissipate energy.
• In order to reach the top of
the cliff, the man had to use
energy to work against
gravity.
• This energy used as work is
recovered as KE by diving.
• Upon reaching the water,
his speed gives him kinetic
energy equal to the work he
used to climb upward.
• In general, a force is conservative if the work
it does moving an object between two points
is the same regardless of the path taken.
• Potential energy is the stored energy that
results from an object’s position or condition.
 It depends only on the beginning and ending
points of motion…not the path taken.
• Gravitational PE – potential energy stored in the
gravitational fields of interacting bodies
 product of an objects mass, gravitational acceleration,
and height.
Gravitational Potential Energy:
PEg = mgh
*Can also be expressed as “weight x height”
• The work done by gravity is the negative of
the change in gravitational potential energy.
Work done by gravity:
Wg = -( PEf – PEi ) = -( mghf – mghi )
Gravitational Potential Energy
Example
• A spoon is raised 21.0cm above a table. If
the spoon and its contents have a mass of
30.0g, what is the gravitational potential
energy associated with the spoon at that
height relative to the surface of the table?
Bellringer 11/1
• A student slides a 0.75kg textbook across
a table, and it comes to rest after traveling
1.2m. Given the coefficient of kinetic
friction between the book and the table is
0.34, use the work-kinetic energy theorem
to find the book’s initial speed?
• Elastic Potential Energy – energy available
when a deformed elastic object returns to its
original configuration
Elastic Potential Energy:
PEelastic = ½ kx2
k = spring/force constant
x = distance compressed/stretched
Example
• A 70.0kg stuntman is attached to a
bungee cord with an unstretched length of
15.0m. He jumps off a bridge spanning a
river from a height of 50.0 m. When he
finally stops, the cord has a stretched
length of 44.0m. Treat the stuntman as a
point mass, and disregard the weight of
the bungee cord. Assuming the spring
constant of the bungee is 71.8N/m, what is
the total potential energy relative to the
water when the man stops falling?
Example continued
Given:m = 70.0 kg
k = 71.8 N/m
g = 9.81 m/s2
h = 50.0 m – 44.0 m = 6.0 m
x = 44.0 m – 15.0 m = 29.0 m
PE = 0 J at river level
Unknown:
PEtot = ?
Example
• A 2.00kg ball is attached to a ceiling by a
string. The distance from the ceiling to the
center of the ball is 1.00m, and the height
of the room is 3.00m. What is the
gravitational potential energy associated
with the ball relative to each of the
following?
 The ceiling
 The floor
 A point at the same elevation as the ball
Example
• 1. A cart is loaded with a brick and pulled at
constant speed along an inclined plane to the
height of a seat-top. If the mass of the loaded cart
is 3.0 kg and the height of the seat top is 0.45
meters, then what is the potential energy of the
loaded cart at the height of the seat-top?
• 2. If a force of 14.7 N is used to drag the loaded
cart (from previous question) along the incline for
a distance of 0.90 meters, then how much work is
done on the loaded cart?
Conservation of Energy
• The Law of Conservation of Energy states:
ENERGY CAN NEVER BE CREATED OR DESTROYED.
• Mechanical Energy (ME)
 Sum of kinetic energy and all forms of
potential energy
 ME = KE + ∑PE
• Applying this to KE and PE, we develop the Law of
Conservation of Mechanical Energy:
 The total mechanical energy of an isolated
system will remain constant.
Conservation of Mechanical Energy:
KEi + PEi = KEf + PEf
If gravity is the only force doing work:
½mv2i + mgyi = ½mv2f + mgyf
From the Law of Conservation of Energy, we know that:
KEi + PEi = KEf + PEf
We can expand this to:
½mvi2 + mghi = ½mvf2 + mghf
Suppose an object held at rest at some initial
height is dropped, and allowed to impact
the ground. Rearrange the above equation
to solve for the final velocity of the object
(at the moment when it impacts).
Example
• Starting from rest, a child zooms down a
frictionless slide from an initial height of
3.00m. What is her speed at the bottom of
the slide? Assume she has a mass of
25.0kg.
Example
• You are designing a roller coaster in which
a car will be pulled to the top of a hill of
height h and then, starting from a
momentary rest, will be released to roll
freely down the hill and toward the peak of
the next hill, which is 1.1 times as high.
Will your design be successful? Explain
your answer.
1.
2.
3.
Explain how work and energy are related (aside
from having the same unit).
Use the picture to describe the changes in
energy that take place between each point on
the coaster.
Which point on the coaster will have the highest
KE? Explain.