Work Done by a Constant Force
The definition of work
Work for Force at an Angle
If the force is at an angle to the displacement:
Negative and Positive Work
The work done may be
Net Work
The sum of all the work done
by all forces is
If the person lifts the box with the same force
as the weight of box, the box will move at
constant speed. Net work is zero. Why?
Perpendicular Force and Work
A car is traveling on a curved
highway. The force due to
friction points toward the center
of the circular path.
How much work does the
frictional force do on the car?
Example:
A rope inclined upward at
45o pulls a 15kg suitcase
through the airport. The
tension on the rope is 85N.
a) How much work does the tension do if the
suitcase is pulled 50m?
b) How much work does the normal force do on
suitcase?
c) If uk= 0.25 between the suitcase and floor,
find the net work done on the suitcase.
Force vs Distance Graph
Find the work done by
the force from 0-6.0m
ENERGY
Energy is
Work can also be defined
Energy is a
Work-Energy theorem
If the net work done on an object
A) Kinetic Energy
Kinetic Energy is the
Example:
A 2200 kg truck encounters an average friction
force of 785N at interstate speeds. Suppose the
truck accelerates from 25m/s to 35m/s over a
distance of 350m. Determine the amount of force
generated by the truck’s drive-train in order to
produce this result.
A paratrooper fell 370m after jumping from an aircraft
without his parachute opening. He landed in a
snowbank, creating a crater 1.1m deep, but survived
with only minor injuries. Assuming the paratrooper‘s
mass was 80kg and his terminal velocity was 50m/s,
estimate __________.
a) the net work done on the paratrooper as the crater was
created (beginning with his striking the snow)
b) the work done by the snow
c) the average force exerted on him by the snow to stop him
d) the work done on him by air resistance from plane to initial
contact with snow. DO NOT assume terminal v for entire fall.
A 230-kg load is lifted 18.0m vertically upward with an
acceleration of a = 0.180g by a single cable.
Determine the __________.
a) tension in the cable
b) net work done on the load
c) work done by the cable on the load
d) work done by gravity on the load
e) final speed of the load assuming it started from rest.
B) Gravitational Potential Energy
Springs
Springs can exert forces on objects.
Pull on a spring, it pulls back. Push
on a spring, it pushes back.
Force exerted by a spring
is given by Hooke’s Law:
C) Elastic Potential Energy
As a spring is
stretched or
compressed
Fmax
x
But since spring force
Force versus Stretch of 3 different Springs
What is the
significance of
the slopes of
the 3 graphs?
EXAMPLE
A block of mass 0.750 kg is free to move on a
horizontal surface where μ = 0.250. As shown in
the diagram below, the block is placed against a
spring with constant k = 83.0 N/m. The spring is
compressed 0.20 m and then the block is
released. Find the speed of the block just as it
leaves the spring.
EXAMPLE: A 350-g mass is hung from a 32.5cm
long vertical spring causing its length to
increase to 41.75cm.
a)Determine the elastic potential energy of the
system after the mass has stretched the spring
and reached equilibrium.
b)Calculate the change in total potential energy of
the system at this point. Refer to equilibrium as
zero point.
Assume someone pulls the mass down, stretching the spring
an additional 9.25cm and releases the mass.
c) Determine the speed of mass when it returns to the original
equilibrium point.
Conservative & Non-Conservative Forces
A conservative force is a force with the
property that the work done in moving a
particle between two points is independent
of the path taken…only matters on initial and
final positions. ie; Gravity & spring force.
A non-conservative force is a force with
the property that the work done in moving
a particle between two points DOES
depend on the path taken. ie; friction
For example, moving ball along the vertical path or curvey
path still results in the same PEg gained or work done by
gravity. However the work done by air friction would be
different for the 2 different paths.
Conservation of Mechanical Energy
The total energy
Energy is
If friction is present
Einitial = Efinal
Power
Involves the rate
Example1
A kid throws a 4.90N rock off a bridge that is 25.0m
above the water. The initial velocity is 13.0m/s at 0°.
Find the rock's speed as it hits the water.
Example2
A girl with mass 28kg climbs a ladder to the top of a
slide, 4.8m high. She slides down the slide and
reaches a speed of 3.2m/s at the
bottom. Determine the work done by friction.
Example3
A spring with constant k = 2500 N/m is mounted vertically and
then compressed 10.0 cm. A 250 gram ball is placed on top of
the spring and then the ball and spring are released. At what
height above equilibrium will the ball be moving at 4.0m/s?
Example4
A block of wood with mass 0.50 kg is initially at rest on an
incline of 30o where μk = 0.30. A person gives the block a
quick push up the incline, parallel to surface, and lets go. The
block slides a total distance of 2.0 m from beginning to end
before stopping. Find the speed of the block at release.
Example5
An engine moves a boat through the water at a
constant speed of 15m/s. The engine must
develop a thrust of 6.0kN to balance the force of
drag from the water acting on the hull. Determine
the power output of the engine.
Example6
A dart gun has a spring with a spring constant of
297.5 N/m and is positioned 3.0m above the floor. A
35.0-g dart depresses the spring 6.50 cm and is
locked into place until the trigger releases it. The
gun is pointed fired horizontally. How high above the
ground will the speed of the dart be 8.4m/s?