Download Review of Mechanics

ELE 100 Introduction to Engineering
Mechanics 1
Q: What is mass?
A: A fundamental unit expressing the amount of “stuff” an object has. In the international
system of units, mass is measured in kilograms, distance is measured in meters, and time
is measured in seconds.
Q: What is velocity?
A: The distance an object moves in a certain time. In SI units, velocity is measured in
meters per second.
Q: What is acceleration?
A: The rate of change of velocity in a certain time. In SI units, acceleration is measured
in meters per second per second.
Q: What is force?
A: A push or a pull. Force is defined in terms of the fundamental SI units.. A force of one
Newton is the force that accelerates a mass of one kilogram at the rate of one meter per
second per second.
F = Ma
Newtons kilograms m/s/s
Q: What is weight?
A: The force on an object resulting from the attraction of one mass to another. Newton
discovered that the gravitational attraction between two objects is proportional to the
product of the masses and inversely proportional to the distance between their centers of
gravity.
F = kM1M2
R2
That gravitational attraction results in an acceleration of each mass toward the other. If
one of the objects is the earth with mass M1 and radius R, then the acceleration of an
object of mass M2 toward the earth is:
F = g M2 or F = M2 g
Where g is the combination of kM1 and equals 9.81 meters per second per second.
R2
Weight of an object near the surface of the earth is therefore the mass of the object times
the acceleration of gravity F = mg, where W is in newtons, m is the mass of the object in
kilograms, and g is 9.81 meters per second per second.
Q: What is the weight of a mass of 100 grams?
A: F = 0.1x9.81 = 0.981 newtons
Q: What is work?
A: Mechanical work is defined as the product of the force on an object and the distance
the mass is moved. It does not matter how fast the mass is moved.
Work = Fd
Work and energy are both measured in joules.
1 joule = 1 newton-meter
Q: What work is required to lift a 100 gram mass 60 centimeters?
A: Work = Fh = Mgh = 0.1x9.81x0.6 = 0.59 joules
Q: What is power?
A: The rate of doing work or expending energy, measured in joules per second.
Q: What mechanical power corresponds to lifting a 100 gram mass 60 centimeters in 10
seconds?
A: P = 0.59 joules/10 seconds = 0.059 joules/second.
But we saw with the battery experiments that 1 joule per second equals one watt.
So the mechanical power in this example is 0.059 joules/second = 0.059 watts.
Notice that Work = Fh = mgh
And Power = mgh/t
But h/t is distance/time or velocity = v
So Power = mgv if we are lifting something of mass m at a velocity v near the surface of
the earth.
Q: What is efficiency?
A: The ratio of the output to the input times 100 to convert to percent efficiency.
The output and the input need to be in the same units. If we use power as the quantity of
interest and watts as the units, we can find the efficiency of an electromechanical system
by dividing the output mechanical power by the electrical input power.
Efficiency = (Pout/Pin)x100