# Kinetic Energy

Mechanics

Oct 29, 2013 (4 years and 8 months ago)

146 views

EA 2

2011

Mechanical Engineering

What is Mechanical Engineering?

Mechanical engineering is the second largest and
one of the oldest disciplines; broadest of all
engineering disciplines.

Mechanical engineers apply the principles of
mechanics and energy to the design of machines
and devices:

ENERGY

and
MOTION

What will you study as an ME student?

Forces, motion, structures
: statics, dynamics, kinematics,
mechanics of solids and fluids.

Energy
: thermodynamics, heat transfer

Materials
: materials engineering & processing, manufacturing.

Machines
: graphics, design, machine elements, controls.

Economics
: engineering economic analysis, cost engineering.

Human and Social Studies
: arts, humanities, social sciences,
history, government, ethics, law.

Overall foundation
: math, physics, chemistry, biology, analysis
skills, communication skills, computation skills.

Mass vs. Weight

A 1.0
-
kg mass is suspended from a
spring scale in an effort to determine
its weight. The scale reads just short
of 10.0 N
-

close enough to call it
9.8 N.

Mass

refers to
how much stuff

is
present in the object.

Weight

refers to the force with
which gravity pulls upon the object

F = m * a

9.81 N/m
2

Check Understanding

1. Complete the following table showing the relationship between mass and weight.

Object

Mass (kg)

Weight (N)

Melon

1 kg

9.8 N

Apple

.1 kg

0.98 N

Pat

25 kg

245 N

Fred

100 kg

980 N

2. Different masses are hung on a spring scale calibrated in Newtons.

a.
The force exerted by gravity on 1 kg = 9.8 N.

b.
The force exerted by gravity on 5 kg = __
49
____ N.

c.
The force exerted by gravity on __
10
_____ kg = 98 N.

d.
The force exerted by gravity on 70 kg = ___
686
____ N.

Energy and Momentum

Work and Energy

Machines and Mechanical Advantage

Work

Energy and Conservation of Energy

1.
Calculate the mechanical advantage for a lever or rope
and pulleys.

2.
Calculate the work done in joules for situations
involving force and distance.

3.
Give examples of energy and transformation of energy
from one form to another.

4.
Calculate potential and kinetic energy.

5.
Apply the law of energy conservation to systems
involving potential and kinetic energy.

Objectives

machine

energy

input force

output force

ramp

gear

screw

rope and pulleys

closed system

work

lever

friction

mechanical system

simple machine

potential energy

kinetic energy

chemical energy

mechanical energy

mechanical
advantage

joule

energy

conservation of
energy

electrical energy

input output

input arm output

arm

fulcrum

Vocabulary Terms

Key Question:

How do simple
machines work?

Machines and Mechanical
Advantage

The ability of humans to build buildings and
move mountains began with our invention
of
machines
.

In physics the term “
simple machine

means a machine that uses only the forces
directly applied and accomplishes its task
with a single motion.

Machines

The best way to analyze what a machine
does is to think about the machine in terms
of
input

and
output
.

Machines

Mechanical Advantage

Mechanical advantage

is the
ratio of output force to input
force.

For a typical automotive jack the
mechanical advantage is 30 or
more.

A force of 100
newtons

(22.5
pounds) applied to the input arm
of the jack produces an output
force of 3,000
newtons

(675
pounds)

enough to lift one
corner of an automobile.

Mechanical Advantage

MA =
F
o

F
i

Output force (N)

Input force (N)

Mechanical

advantage

Mechanical Advantage of a Lever

MA
lever

=
L
i

L
o

Length of input arm

(m)

Length of output arm

(m)

Mechanical

advantage

Calculate position

Where should the fulcrum of a lever be
placed so one person weighing 700 N
can lift the edge of a stone block with a
mass of 500 kg?

The lever is a steel bar three meters long.

Assume a person can produce an input force equal to
their own weight.

Assume that the output force of the lever must equal
half the weight of the block to lift one edge.

Wheels, gears, and rotating
machines

Axles and wheels provide advantages.

Friction occurs where the wheel and axle touch or where the wheel
touches a surface.

Rolling motion creates less wearing away of material compared with
two surfaces sliding over each other.

With gears the trade
-
off is
made between
torque

and
rotation speed.

An output gear will turn with
more
torque when it rotates
slower than the input gear.

Ramps and Screws

Ramps

reduce input force by
increasing the distance over
which the input force needs to
act.

A
screw

is a simple machine that
turns rotating motion into linear
motion.

A thread wraps around a screw at
an angle, like the angle of a
ramp.

Work

Key Question:

What are the
consequences of
multiplying forces in
machines?

Work

In physics,
work

has a very specific
meaning.

In physics, work
represents a
measurable change

in a system, caused
by a
force.

Work

If you push a box with a force of
one
newton

for a distance of
one meter
, you
have done exactly
one joule

of work.

Work (force is parallel to distance)

W = F x d

Distance (m)

Force (N)

Work (joules)

Work (force at angle to distance)

W = Fd cos (
q
)

Distance (m)

Force (N)

Work (joules)

Angle

Work done against gravity

W =
mgh

Height object raised (m)

Gravity (m/sec
2
)

Work (joules)

Mass (g)

Why the path doesn't matter

Calculate work

A crane lifts a steel beam with
a mass of 1,500 kg.

Calculate how much work is
done against gravity if the
beam is lifted 50 meters in
the air.

How much time does it take
to lift the beam if the motor of
the crane can do 10,000
joules of work per second?

Energy and Conservation of Energy

Energy

is the ability to make things change.

A system that has energy has the ability to do work.

Energy is measured in the same units as work
because energy is transferred during the action of
work.

Potential Energy

E
p

= mgh

Height (m)

Mass (kg)

Potential Energy

(joules)

Acceleration

of gravity (m/sec
2
)

A cart with a mass of
102 kg is pushed up a
ramp.

The top of the ramp is
4 meters higher than
the bottom.

How much potential
energy is gained by the
cart?

If an average student
can do 50 joules of
work each second, how
much time does it take
to get up the ramp?

Potential Energy

Energy of motion is called
kinetic energy
.

The kinetic energy of a moving object depends on
two things: mass and speed.

Kinetic energy is proportional to mass.

Kinetic

Energy

Mathematically, kinetic energy increases as the
square

of speed.

If the speed of an object doubles, its kinetic
energy increases four times. (mass is constant)

Kinetic

Energy

E
k

=
1

mv
2

2

Speed (m/sec)

Mass (kg)

Kinetic Energy

(joules)

Kinetic

Energy

Kinetic energy becomes important in calculating
braking distance.

Kinetic Energy

A car with a mass of 1,300
kg is going straight ahead at
a speed of 30 m/sec (67
mph).

The brakes can supply a
force of 9,500 N.

Calculate:

a) The kinetic energy of the car.

b) The distance it takes to stop.

Calculate Kinetic Energy

As energy takes different forms and changes things
by doing work, nature keeps perfect track of the
total.

No new energy is created and no existing energy is
destroyed.

Law of Conservation of Energy

Energy and Conservation of Energy

Key Question:

How is motion on a
track related to
energy?