WEP - Measurement and Units Flashcards
When is work said to be done?
Only when the force applied on the body makes the body move (i.e., there is a displacement of the body) in the direction of the force applied
Name the two factors on which the amount of work done depends
- the magnitude of the force applied
2. the displacement produced by the force
What is the amount of work done equal to?
The product of the force and the displacement of the point of application of the force in the direction of the force
Give the formula for the amount of work done
W = F X S
In the eqn. W = F X S, what does “X” mean?
It means simple multiplication of the two scalars F and S which are the magnitudes of force and displacement respectively. It does not mean the cross or vector product of two vectors F and S (arrows)
When is no work said to be done?
If a force acts on a body and the body does not move i.e., displacement is zero, then no work is done
Is work a scalar or a vector quantity? Why?
Scalar, because direction is not needed to fully express the amount of work done
Name the ways in which we can determine the amount of work done if the force displaces the body in a direction other than that of the force
- By finding the component of displacement along the
force - By finding the component of force along the
displacement
What is the formula for finding the work by finding the component of displacement along the force?
W = F X S cos θ
W = Force X component of displacement in the
direction of force
What is the formula for finding the work by finding the component of force along the displacement?
W = F cos θ X S
W = Component of force in the direction of
displacement X displacement
In vector form, what is the work done W written as?
W = F (arrow) ⋅ S (arrow)
What does the dot product mean?
The scalar product
Why is work expressed as the dot product of force and displacement vectors?
Because force F and displacement S are vector quantities and work W is a scalar quantity
Is the dot product of 2 vectors scalar or vector?
Scalar
Name the three factors the work done depends on, in the case that displacement is not in direction of force
- The magnitude of force
- The magnitude of displacement
- The angle between the force and displacement
What happens to the angle bet. the 2 when displacement is in direction of the force?
θ = 0°, then cos 0°= 1 W = F X S, the work done is positive
When is the work done positive?
If the displacement is in direction of force, i.e., θ = 0°, then cos 0° = 1 → W = F X S
Why is the work done in a free-falling body positive?
In free fall of a body of mass m under gravity through a height h from A to B, the force of gravity F (=mg) is in the direction of displacement S (=h) and the work done by the force of gravity is W = FS = mgh
Why is W done by the centripetal force zero in the case of a body revolving in a circular path?
A body that revolves in a circular path under the influence of the centripetal force, on completing one round, the displacement becomes zero, so the work done by the centripetal force is zero
What is θ when the displacement is normal to the direction of force?
90°, then cos 90°=0
∴ W = 0
Why is no work done when a coolie walks on horizontal ground while carrying a load on his head?
No work is done against the force of gravity because the displacement of load is normal to the direction of the force of gravity which is vertically downwards.
Against which force does the coolie work when he moves with the load?
Against the force of friction
What remains constant in a body moving in a circular path despite which factor?
The kinetic energy and the speed of the body does not change although a force acts on the body
Why does the kinetic energy and speed of the body not change although a force acts on the body in a circular path?
When a body moves in a circular path in a horizontal plane, no work is done since centripetal force on the body at any instant is along the tangent to the circular path, i.e., normal to the direction of force on the body (i.e. θ = 90 °). It is for this reason that the KE and speed do not change despite centripetal force.
Name the 2 situations in which the amount of work done by a force is zero
1) When there is no displacement
(i. e., S = 0)
2) When the displacement is normal to the direction
of force (i.e., θ = 90 °)
What is θ if displacement is in a direction opposite to the force?
θ = 180 °, then cos 180 ° = -1
∴ W = -F X S
When is the work done negative?
When the force opposes the motion or it tries to stop a moving body
Why is the work done negative when a body moves on a surface?
The force of friction between the body and the surface is in a direction opposite to the motion of the body (i.e. θ = 180 °). This, work done by force of friction is negative
Why is work done negative when a ball of mass m is thrown upwards?
When a ball of mass m is thrown upwards from A to B to a height h, the displacement h is opposite to the direction of force of gravity mg, so the work done by the force of gravity mg in displacement h is
W = -mgh i.e., negative
How is work done determined if the force is variable?
If the force varies during displacement, the work done is determined by plotting a force-displacement graph
In a force displacement graph, on which axis is force taken and on which axis is displacement taken?
The force is taken on the Y-axis and the displacement S (in direction of the force) is taken on the X-axis.
In which direction is displacement S taken on X axis?
In the direction of force
In a force displacement graph, what gives the work done?
The area enclosed by the sketch and the displacement axis (i.e. X axis) gives the work done
What kind of force-displacement graph will be obtained if force is constant?
The graph will be a straight line parallel to the X-axis, and the area of the rectangle OABC (= F X S), enclosed between the straight line and the X-axis, will be equal to the work done.
How to find out work done when the graph for force against displacement is an inclined straight line?
The work done by the force in displacement S is equal to the area of the triangle OAB ( = 1/2 F X S)
Give the formula for the work done by the force of gravity on a body
W = FS = mgh
Give the formula for the force of gravity on a body
F = mg
Work done by the forces of gravity is the same whether the body comes down from a certain height using _ or slope or a _
Stairs, slope, lift
Calculate the vertical displacement in the direction of the force for stairs.
For stairs, h = no. of stairs * height of each stair
What is the SI unit of work and its abbreviation?
SI unit for work is Joule. Abbreviated as J
What is the value of 1 joule?
Work = force X displacement
∴ 1 joule = 1 newton X 1 metre
Define 1 joule
Joule is the SI unit of work. 1 joule of work is said to be done when a force of 1 newton displaces a body through a distance of 1 metre in its own direction
Name the bigger units of work and give their values
kilo - joule (kJ) = 10^3 J
mega - joule (MJ) = 10^6 J
giga-joule (GJ) = 10^9 J
What is the biggest unit of joule?
giga-joule (GJ) = 10^9 J
What is the CGS unit of work?
1 erg
What is the value of 1 erg?
1 erg = 1 dyne X 1 cm
Define 1 erg of work
1 erg of work is said to be done when a force of 1 dyne displaces a body through a distance of 1 cm in its own direction
Give the relationship between joule and erg
1 joule = 1 N X 1 m
But 1 N = 10 ^ 5 dyne and 1 m = 10 ^ 2 cm
∴ 1 joule = 10 ^ 5 dyne X 10 ^ 2 cm
= 10 ^ 7 dyne X cm = 10 ^ 7 erg
Thus 1 joule = 10 ^ 7 erg
Define power
The rate of doing work is called power
Is power a scalar or vector quantity?
Scalar
How is power measured?
The power spent by a source is measured as the amount of work done by the source in one second (or it is equal to the rate of doing work by the source)
Give the formula for power
P = W/t
Name the 2 factors on which power depends
- the amount of work done by the source
2. the time taken by source to do said work
When is more power spent by a person?
If a machine or person does a given amount of work in less time, more power is spent by it
Explain the formula P = F X v
If a constant force F acts on a body and it displaces the body by a distance S (in the direction of force) in time t, then work done W = F X S P = W/t = F X S/t Since S/t= v (avg. speed) ∴ P = Force X Average speed P = F X v
Give the SI unit fo power
Watt, abbreviated as W
Define 1 watt
If 1 joule of work is done in 1 second, the power spent is said to be 1 watt
Give the value of 1 watt
1 watt = 1 joule/ 1 second = 1 J s ^ -1
Name the bigger units of power and give their value
kilowatt (kW) = 10^3 W
megawatt (MW) = 10^6 W
gigawatt (GW) = 10^9 W
Name the smaller units of power
1 milliwatt (mW) = 10 ^ -3 watt 1 microwatt (µW) = 10 ^ -6 watt
Give the CGS unit of power
erg per second (erg s ^ -1)
Give the relationship between SI & CGS units
1 W = 1 J s ^ -1 = 10 ^ 7 erg s ^ -1
Name the unit of power largely used in mechanical engineering
Horse power ( H.P)
How is 1 H.P. related to the SI unit watt?
1 HP = 746 W = 0.746 kW
Give 3 differences between work and power
- Work done by a force is equal to the product of force
and displacement in the direction of force. - Power of a source is the rate of work done by the
force. - Work done does not depend on time.
- Power spent depends on the time in which work is
done. - SI unit of work is joule (J)
- SI unit of power is watt (W)
Define energy
The energy of a body is its capacity to do work
What kind of quantity is energy?
Energy is a scalar quantity
How are work and energy related?
Whenever work is done, there is a transfer of energy. When a body does work, its energy decreases whereas when work is done on the body, its energy increases
When is there no transfer of energy?
When a body is acted upon by a force normal to the direction of its displacement
Why is there no transfer of energy for a body moving in a circular path?
Centripetal force is normal to its displacement and work done is zero i.e., there is no transfer of energy.
Give the SI & CGS units of energy
SI unit of energy is joule (J)
CGS unit of energy is erg
Give the relationship between joule and erg
1 J = 10^7 erg
Give the bigger units of energy
- watt hour (Wh)
2. kilowatt hour (kWh)
Define 1 watt hour
1 Wh is the energy spent (or work done) by a source of power 1 W in 1 h , i.e.,
1 watt hour = 1 watt * 1 hour
= 1 J s^-1 * 3600 s
= 3600 J = 3.6 kJ
1 watt hour = _ J = _ kJ
3600 J, 3.6 kJ
Define kilowatt hour
One kilowatt hour (1 kWh) is the energy spent (or work done) by a source of power 1 kW in 1 h. i.e.,
1 kWh = 1 kilowatt * 1 hour
= 1000 J s^-1 * 3600 s
= 3.6*10^6 J = 3.6 MJ
1 kWh = _ J = _ MJ
3.6*10^6 J = 3.6 MJ
Heat energy is usually measured in which unit?
Calorie
Define 1 calorie
1 calorie is the heat energy required in raising the temperature of 1 g of water from 14.5 C to 15.5 C (or through 1 C)
How is calorie related to joule?
1 J = 0.24 calorie or 1 calorie = 4.18 J
Name a bigger unit of heat energy
I kilocalorie = 1000 calorie = 4180 J
What is the energy transfer in case of atomic particles measured in?
electron volt (eV)
Define 1 eV
1 eV is the energy gained by an electron when it is accelerated through a potential difference of 1 volt. i.e.,
1 eV = charge on an electron X volt
= 1.6 X 10 ^ -19 coulomb x 1 volt
= 1.6 10 ^ -19 joule
1 eV = _ J
1 eV = 1.6 10 ^ -19 joule
Give 3 differences between energy and power
- Energy of a body is its capacity to do work
- Power of a source is the rate at which energy is supplied by it
- Energy spent does not depend on time
- Power depends on the time in which energy is spent
- SI unit of energy is joule (J)
- SI unit of power is watt (W)
