(a) Explain with the aid of a diagram what is meant by the moment of a force about a point. (b) State the conditions of equilibrium for a number of coplanar...
(a) Explain with the aid of a diagram what is meant by the moment of a force about a point.
(b) State the conditions of equilibrium for a number of coplanar parallel forces.
A metre rule is found to balance at the 48cm mark. When a body of mass 60g is suspended at the 6cm mark, the balance point is found to be at the 30cm mark. Calculate:
(i) the mass of the metre rule; (ii) the distance of the balance point from the zero end, if the body were moved to the 13cm mark.
(c) Show that the efficiency E, the force ratio M.A and the velocity ratio V.R of a machine are related by the equation \(E = \frac{M.A}{V.R} \times 100%\)
The efficiency of a machine is 80%. Determine the work done by a person using this machine to raise a load of 200kg through a vertical distance of 3.0m.
[Take g = 10ms\(^{-2}\)]
(a) Moment of a force about a point
The moment of a force is its turning effect about a pivot or point. It is given by:
\[ \text{Moment} = F \times d \]
where \(F\) is the force and \(d\) is the perpendicular distance from the pivot to the line of action of the force. The SI unit is newton metre, \(\text{N m}\).
The distance used is not simply any distance from the pivot to the force: it must be measured at right angles to the force's line of action.
(b) Conditions for equilibrium of coplanar parallel forces
The total force in one direction equals the total force in the opposite direction, so the resultant force is zero.
The sum of clockwise moments about any point equals the sum of anticlockwise moments about that point, so the resultant moment is zero.
Metre rule calculation
Since the metre rule balances by itself at the \(48\,\text{cm}\) mark, its weight acts at the \(48\,\text{cm}\) mark.
When the \(60\,\text{g}\) body is at \(6\,\text{cm}\), the pivot is at \(30\,\text{cm}\).
Distance of the \(60\,\text{g}\) mass from the pivot: \(30-6=24\,\text{cm}\).
Distance of the rule's weight from the pivot: \(48-30=18\,\text{cm}\).
Taking moments about the balance point:
\[ 60 \times 24 = M \times 18 \]
\[ M=\frac{60\times24}{18}=80\,\text{g} \]
(i) Mass of the metre rule \(=80\,\text{g}\).
For the body at the \(13\,\text{cm}\) mark, let the new balance point be \(x\,\text{cm}\) from the zero end. The body is to the left of the pivot and the rule's weight acts to the right:
\[ 60(x-13)=80(48-x) \]
\[ 60x-780=3840-80x \]
\[ 140x=4620 \]
\[ x=33\,\text{cm} \]
(ii) The balance point is \(33\,\text{cm}\) from the zero end.
(c) Relationship between efficiency, mechanical advantage and velocity ratio
The moment of a force is its turning effect about a pivot or point. It is given by:
\[ \text{Moment} = F \times d \]
where \(F\) is the force and \(d\) is the perpendicular distance from the pivot to the line of action of the force. The SI unit is newton metre, \(\text{N m}\).
The distance used is not simply any distance from the pivot to the force: it must be measured at right angles to the force's line of action.
(b) Conditions for equilibrium of coplanar parallel forces
The total force in one direction equals the total force in the opposite direction, so the resultant force is zero.
The sum of clockwise moments about any point equals the sum of anticlockwise moments about that point, so the resultant moment is zero.
Metre rule calculation
Since the metre rule balances by itself at the \(48\,\text{cm}\) mark, its weight acts at the \(48\,\text{cm}\) mark.
When the \(60\,\text{g}\) body is at \(6\,\text{cm}\), the pivot is at \(30\,\text{cm}\).
Distance of the \(60\,\text{g}\) mass from the pivot: \(30-6=24\,\text{cm}\).
Distance of the rule's weight from the pivot: \(48-30=18\,\text{cm}\).
Taking moments about the balance point:
\[ 60 \times 24 = M \times 18 \]
\[ M=\frac{60\times24}{18}=80\,\text{g} \]
(i) Mass of the metre rule \(=80\,\text{g}\).
For the body at the \(13\,\text{cm}\) mark, let the new balance point be \(x\,\text{cm}\) from the zero end. The body is to the left of the pivot and the rule's weight acts to the right:
\[ 60(x-13)=80(48-x) \]
\[ 60x-780=3840-80x \]
\[ 140x=4620 \]
\[ x=33\,\text{cm} \]
(ii) The balance point is \(33\,\text{cm}\) from the zero end.
(c) Relationship between efficiency, mechanical advantage and velocity ratio
