Transcript Psc CH-10 Work_ Energy_ _ Machines

Chapter 10
Energy, Work, &
Simple Machines
Energy
•The ability to
produce change
Energy
•The ability
to do work
Types of Energy
•Kinetic
•Potential
Kinetic Energy (K)
•The energy of
motion
Potential
Energy (U)
•Stored energy
Kinetic Energy
2
2
•vf = vi + 2ad
•vf - vi = 2ad
2
2
Kinetic Energy
•a = F/m
2
2
•vf - vi = 2Fd/m
Kinetic Energy
½ mvf - ½ mvi
2
= Fd
2
Kinetic Energy
K = ½ mv
2
Potential Energy
U = mgh
Work (W)
•The process of
changing the
energy of a system
Work
•The product of
force times
displacement
Work
•W = Fd
Work-Energy
Theorem
•W = DK
Calculate the work
required to lift a
50.0 kg box to a
height of 2.0 m:
Calculate the work
done when a 250 N
force is applied to
move a cart 40.0
km:
Calculate the work
required to push a
500.0 kg box 250 m at
a constant velocity.
m = 0.20 between the
box & the floor.
Constant force
at an Angle
Direction of movement
a
Constant force
at an Angle
W = F(cos a)d
Calculate the work done
when mowing the lawn
when a boy applied a
o
50.0 N force at a 37
from horizontal for 2.0
km.
Calculate the work done
when a girl pulls a 4.0
kg box with a rope at a
o
37 from horizontal for
2.0 m. m = 2.5
Power
•The rate of
doing work
Power
•P = W/t
A 25 Mg elevator
rises 125 m in 5.0
minutes. Calculate:
F, W, & P
A 10.0 Gg crate is
accelerated by a cable
o
up a 37 incline for 50.0
m in 2.5 hrs. m = 0.20
Calculate: FT, W, & P
A 50.0 g box is
o
accelerated up a 53
incline for 50.0 m at 250
2
cm/s . m = 0.20
Calculate: FA, vf,W, P, K,
& U at the top of the ramp
Machines
• Devices used to ease force
one has to apply to move an
object by changing the
magnitude and direction of
the force.
Machines
• Machines do not reduce the
work required, but do
reduce the force required.
Machines
•The force applied is
called the effort
force (Fe).
Machines
•The force exerted by
the machine is called
the resistant force
(Fr).
Mechanical
Advantage
• The ratio of resistant
force to effort force
Mechanical
Advantage
Fr
MA = F
e
In an Ideal Situation
•100 % of the work
input into a system
would be transferred
to output work, thus:
Wo = Wi or
Frdr = Fede or
Fr/Fe= de/dr
Ideal Mechanical
Advantage
de
IMA = d
r
Efficiency
•The ratio of output
work to input work
times 100 %
Efficiency =
Wo
X 100 %
Wi
Efficiency =
MA
X 100 %
IMA
Simple Machines
Lever Inclined plane
Wedge Wheel & Axle
Screw Pulley
Lever
Fr
dr
de
Fe
Fr
dr
de
Fe
IMA = de/dr =
length de/length dr
Inclined Plane
de
dr
Fr
Fe
de
dr
Fr
Fe
a
IMA = de/dr =
length hyp/hyp sin a
Wedge
½ Fr
Fe
½ Fr
½ Fr
Fe
½ Fr
a
IMA = de/dr = cot ½ a
Screw
Fe
Fr
Pulley
Fe
Fr
Fe
Fr
IMA = the
number
of lines
pulling up
Wheel & Axle
Fr
Fe
IMA = ratio
of effort wheel
radius/resistant
wheel radius
Fr
Fe
A 100.0 Mg trolley is
pulled at 750 cm/s up a
o
53 inclined railway for
5.0 km. m = 0.20
Calculate: FA,W, P, K, & U
at the top of the ramp
An alien exerts 250 N
on one end of a 18 m
lever with the fulcrum 3
m from a 1200 N load.
Calculate: IMA, MA, &
efficiency
A 350 N force is applied
to push a 50.0 kg box up
o
a 20.0 m ramp at 37
from horizontal.
Calculate: IMA, MA, &
efficiency
A pulley with an
efficiency of 80.0 %
with 5 interconnecting
ropes lifts a 100.0 kg
load. Calculate:
IMA, MA, & FA
A 1.0 m handle is connected to
5.0 cm wheel. The efficiency
of this system is 90.0 %.
Calculate IMA, MA, & the
force required to pull a 500 kg
object connected to the wheel.
A 100.0 cm handle is connected to
5.0 cm wheel with teeth
connecting it to another 50.0 cm
wheel connected to a 2.5 cm axle.
A cable is connected to the axle.
The efficiency of this system is
90.0 %. Calculate IMA & MA
A sledge hammer is used
to apply 25 kN drive a 2.0
cm x 10.0 cm wedge into
a board. Calculate the
force on the board if the
efficiency is 75 %.
Design a system of
simple machines that
can lift at least 100,000
times the force applied
by a human. Assume 90
% efficiency.
The front sprockets on a 21
speed bike are 24 cm, 18 cm,
& 15 cm in diameter. The
back sprockets range from 12
cm to 4.0 cm. Determine the
ratio of highest to lowest
gears.
On the same bike, the wheels
are 80.0 cm in diameter.
Calculate the speed in the
lowest & highest gears if a
person can pedal at 1.0
revolution per second.
A 100.0 kg block (m = .20)
slides from rest down a
o
50.0 m ramp at 37 from
horizontal. At the bottom
of the ramp, it collides with
a 25 kg box (m = .25) &
stops. Calculate:
Answer the questions
on page 175 & work
Problem Section A on
pages 175 & 176.
The 1.0 m crank is turned lifting the
box to a height of 50.0 cm in 5.0
minutes with an efficiency of 90 %.
Calculate: IMA, MA, di, FA, Wo, Wi, &
P.
10.0 m
r = 5.0 cm
1.0 Mg
2.0 m
A 50.0 Mg elevator
is raised 200.0 m in
3.0 minutes at a
constant speed.
Calculate: FAupward, W,
&P
A 200.0 kg sled (m =
0.10) slides from rest
down a 500.0 m incline
o
at 37 from horizontal.
Calculate: F,F//, Ff, Fnet,
a, t, vf, Wo, P, & Kmax