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.