Download Efficiency

Efficiency
Efficiency
• Real machines are not frictionless. Some of the
input energy is dissipated as sound or heat.
• The efficiency of a machine is the ratio of
useful work output to work input.
Wout
eff 
Win
– The efficiency of an ideal
(frictionless) machine is 1, or 100
percent.
– The efficiency of real machines is
always less than 1.
A machine is 75 percent efficient. If
200 joules of work are put into the
machine, how much work output does
it produce?
The work output is 300 joules for a
machine that is 50 percent efficient.
What is the work input?
A person uses a 75-newton force to
push a 51-kilogram car up a ramp. The
ramp is 10 meters long and rises one
meter. Calculate the efficiency.
Simple Machines &
Mechanical Advantage
Mechanical Advantage
• Because the purpose of a simple machine is to change the
direction or magnitude of an input force, a useful way of
characterizing a simple machine is to compare the output
and input force.
• This ratio is called mechanical advantage.
• If friction is disregarded, mechanical advantage can
also be expressed in terms of input and output distance.
Fout
din
MA 

Fin dout
A machine uses an input force of 200
newtons to produce an output force of 800
newtons. What is the mechanical advantage
of this machine?
A machine uses an input force of 200
newtons to produce an output force of 800
newtons. What is the mechanical advantage
of this machine?
Fout = 800 N
Fin = 200 N
MA = 800N/200N = 4
A machine is required to produce an output
force of 600 newtons. If the machine has a
mechanical advantage of 6, what input force
must be applied to the machine?
A machine is required to produce an output
force of 600 newtons. If the machine has a
mechanical advantage of 6, what input force
must be applied to the machine?
Fout = 600 N
MA = 6
Fin = Fout/MA = 600N/6 = 100N
A person lifts a 950 N box by
pushing it up an incline. If the
person exerts a force of 350 N along
the incline, what is the mechanical
advantage of the incline?
A person lifts a 950 N box by
pushing it up an incline. If the
person exerts a force of 350 N along
the incline, what is the mechanical
advantage of the incline?
What is the mechanical advantage
of a lever that allows Jorge to lift a
24-newton box with a force of 4
newtons?
What is the mechanical advantage
of a lever that allows Jorge to lift a
24-newton box with a force of 4
newtons?
A construction worker uses a board and
log as a lever to lift a heavy rock. If the
input arm is 3 meters long and the output
arm is 0.75 meters long, what is the
mechanical advantage of the lever?
A construction worker uses a board and
log as a lever to lift a heavy rock. If the
input arm is 3 meters long and the output
arm is 0.75 meters long, what is the
mechanical advantage of the lever?
Lin = 3 m
Lout = 0.75 m
MA = 3m/0.75m = 4
A child’s toy rake is held so that its
output arm is 0.75 meters. If the
mechanical advantage is 0.33, what is
the input arm length?
A child’s toy rake is held so that its
output arm is 0.75 meters. If the
mechanical advantage is 0.33, what is
the input arm length?
A lever used to lift a heavy box has an
input arm of 4 meters and an output arm
of 0.8 meters. What is the mechanical
advantage of the lever?
A lever used to lift a heavy box has an
input arm of 4 meters and an output arm
of 0.8 meters. What is the mechanical
advantage of the lever?
Mechanical advantage of a ramp
The input work is the input force
multiplied by the length of the
ramp (10 meters). If you set the
input work equal to the output
work, you quickly find that the
input force is 50 newtons (Fd = F
× 10 m = 500 J). The input force
is one-tenth of the output force.
For a frictionless ramp, the
mechanical advantage is the
length of the ramp divided by the
height.
A 5-meter ramp lifts objects to a height
of 0.75 meters. What is the mechanical
advantage of the ramp?
A 5-meter ramp lifts objects to a height
of 0.75 meters. What is the mechanical
advantage of the ramp?
A ramp with a mechanical advantage of
6 is used to move a 36-newton load.
What input force is needed to push the
load up the ramp?
A ramp with a mechanical advantage of
6 is used to move a 36-newton load.
What input force is needed to push the
load up the ramp?
Circular Motion
A bicycle traveled a distance of 100 meters.
The diameter of the wheel of this bicycle is
40 cm. Find the number of rotations of the
wheel.
A bicycle traveled a distance of 100 meters.
The diameter of the wheel of this bicycle is
40 cm. Find the number of rotations of the
wheel.
40 cm = 0.4 m
(2*3.14*0.2 m) = 1.256 m
100 m / 1.256 m = 79.6 rotations
A particle is moving around in a circle
of radius R = 1.5 m with a constant
speed of 2 m/s. What is the angular
velocity of the particle?
A particle is moving around in a circle
of radius R = 1.5 m with a constant
speed of 2 m/s. What is the angular
velocity of the particle?
C = (2*3.14*1.5) = 9.42 m
2 m/s = 120 m per min
120/9.42 = 17.73 rpm
During the spin cycle of a washing machine, the clothes
stick to the outer wall of the barrel as it spins at a rate
as high as 1800 revolutions per minute. The radius of
the barrel is 26 cm.
Determine the speed of the clothes (in m/s) which are
located on the wall of the spin barrel.
Centripetal Force
mass  (tangential speed)
centripetal force =
radius of circular path
2
The maximum speed with which a 945-kg car
makes a 180-degree turn is 10.0 m/s. The radius
of the circle through which the car is turning is
25.0 m. Determine the force of friction acting
upon the car.
A pilot is flying a small plane at 56.6 m/s in a
circular path with a radius of 188.5 m. The
centripetal force needed to maintain the plane’s
circular motion is 1.89 x 10^4 N. What is the
plane’s mass?
A pilot is flying a small plane at 56.6 m/s in a
circular path with a radius of 188.5 m. The
centripetal force needed to maintain the plane’s
circular motion is 1.89 x 10^4 N. What is the
plane’s mass?
m = 1110 kg
A 4.0 kg ball is attached to 0.7 meter
string and spun at 2.0 meters/sec. What
is the centripetal force?
A 4.0 kg ball is attached to 0.7 meter
string and spun at 2.0 meters/sec. What
is the centripetal force?
22.85 N
Gravitational Force
Find the distance between a 0.300 kg billiard ball
and a 0.400 kg billiard ball if the magnitude of the
gravitational force between them is 8.92 x 10-11 N.
Find the distance between a 0.300 kg billiard ball
and a 0.400 kg billiard ball if the magnitude of the
gravitational force between them is 8.92 x 10-11 N.
r= 0.30m
Find the gravitational force a 66.5 kg person
would experience while standing on the surface of
Mars. Mars has a mass of 6.42 x 10^23 kg and a
radius of 3.40 x 10^6 m.