Post on 06-Jan-2016
description
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
•vf2 = vi
2 + 2ad
•vf2 - vi
2 = 2ad
Kinetic Energy•a = F/m
•vf2- vi
2 = 2Fd/m
Kinetic Energy
½ mvf2- ½ mvi
2
= Fd
Kinetic Energy
K = ½ mv2
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-EnergyTheorem
•W = K
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. = 0.20 between the
box & the floor.
Constant force at an Angle
Direction of applied forceDirection of movement
Constant force at an Angle
W = F(cos )d
Calculate the work done when mowing the lawn when a boy applied a 50.0 N force at a 37o
from horizontal for 2.0 km.
Calculate the work done when a girl pulls a 4.0 kg box with a rope at a 37o from horizontal for
2.0 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
up a 37o incline for 50.0 m in 2.5 hrs. = 0.20Calculate: FT, W, & P
A 50.0 g box is accelerated up a 53o
incline for 50.0 m at 250 cm/s2. = 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
Fe
MA =
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
dr
IMA =
Efficiency•The ratio of output work to input work times 100 %
Efficiency =
Wo
Wi
X 100 %
Efficiency =
MAIMA
X 100 %
Simple MachinesLever Inclined plane
Wedge Wheel & Axle
Screw Pulley
Lever
Fe
Fr
dedr
Fe
Fr
dedr
IMA = de/dr = length de/length dr
Inclined Plane
Fe
Fr
dr
de
Fe
Fr
dr
de
IMA = de/dr = length hyp/hyp sin
Wedge
Fe
½ Fr
½ Fr
Fe
½ Fr
½ Fr
IMA = de/dr = cot ½
Screw
Fr
Fe
Pulley
Fe
Fr
Fe
Fr
IMA = the number of lines pulling up
Wheel & Axle
FeFr
FeFr
IMA = ratioof effort wheelradius/resistantwheel radius
A 100.0 Mg trolley is pulled at 750 cm/s up a 53o
inclined railway for 5.0 km. = 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 a 20.0 m ramp at 37o 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 ( = .20) slides from rest down a 50.0 m ramp at 37o from horizontal. At the bottom
of the ramp, it collides with a 25 kg box ( = .25) &
stops. Calculate:
Answer the questions on page 175 & work
Problem Section A on pages 175 & 176.
r = 5.0 cm
10.0 m
2.0 m
1.0 Mg
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.
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 ( = 0.10) slides from rest
down a 500.0 m incline at 37o from horizontal.
Calculate: F,F//, Ff, Fnet, a, t, vf, Wo, P, & Kmax