TEST OF PRACTICAL KNOWLEDGE QUESTION You are provided with a uniform metre rule, a knife-edge, some masses and other necessary materials. i. Determine and r...
You are provided with a uniform metre rule, a knife-edge, some masses and other necessary materials.
i. Determine and record the centre of gravity of the metre rule.
ii. Fix the 100g mass marked N at a point Y, the 80cm mark of the rule using a sellotape.
iii. Suspend another 50g mass marked M at X, a distance A = 1Ocm from the 0cm mark of the rule.
iv. Balance the arrangement horizontally on the knife edge as illustrated in the diagram above.
v. Measure and record the distance B of a knife-edge from the 0cm mark of the rule.
vi. Repeat the procedure for four other values of A =15cm, 20cm, 25cm and 30cm.
vii. Tabulate your readings.
viii. Plot a graph with B on the vertical axis and A on the horizontal axis.
ix. Determine the slope, s, of the graph.
x. Also determine the intercept, c, on the vertical axis.
xi. Evaluate: \(\propto\)) = k\(_{1}\) = (\(\frac{1 - 2s}{s}\))100
(\(\beta\)) = k\(_{2}\) = \(\frac{2c}{s}\) = 160
xii. State two precautions taken to obtain accurate results.
(b)i. Define the moment of a force about a point.
ii. State two conditions under which a rigid body at rest remains in equilibrium when acted upon by non-parallel coplanar forces.
(i) Centre of gravity of the uniform metre rule = 50.0 cm mark (the rule balances horizontally at this point before any mass is added).
The 100 g mass N is fixed with sellotape at the 80 cm mark (point Y); the 50 g mass M is suspended at point X, a distance A from the 0 cm end. The knife-edge is moved until the rule balances horizontally, and B, the distance of the knife-edge from the 0 cm end, is recorded.
Metre rule (fixed 100 g mass N at 80 cm, 50 g mass M at distance A from the 0 cm end) balanced horizontally on the knife-edge at distance B from the 0 cm end.
(vii) Table of readings
S/N
A / cm
B / cm
1
10.0
54.0
2
15.0
55.0
3
20.0
56.0
4
25.0
57.0
5
30.0
57.0
6
35.0
58.0
(viii) Graph of B against A
B is plotted on the vertical axis against A on the horizontal axis and the best straight line is drawn through the points.
B against A: best straight line has slope s = 0.2 and vertical-axis intercept c = 53.0 cm.
(ix) Slope, s
Using two widely-spaced points on the best line, \((A_1,B_1)=(0,\,53.0)\) and \((A_2,B_2)=(30.0,\,59.0)\):
The rule was made to balance exactly horizontal on the knife-edge before each reading of B was taken.
Error due to parallax was avoided by reading the metre rule with the eye placed vertically above the mark being read.
(b)(i) Moment of a force about a point
The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force. Its unit is the newton-metre (N m).
(b)(ii) Two conditions for equilibrium under non-parallel coplanar forces
The vector sum of all the forces is zero (i.e. the algebraic sum of their resolved components in any given direction is zero).
The algebraic sum of the moments of the forces about any point is zero.
(i) Centre of gravity of the uniform metre rule = 50.0 cm mark (the rule balances horizontally at this point before any mass is added).
The 100 g mass N is fixed with sellotape at the 80 cm mark (point Y); the 50 g mass M is suspended at point X, a distance A from the 0 cm end. The knife-edge is moved until the rule balances horizontally, and B, the distance of the knife-edge from the 0 cm end, is recorded.
Metre rule (fixed 100 g mass N at 80 cm, 50 g mass M at distance A from the 0 cm end) balanced horizontally on the knife-edge at distance B from the 0 cm end.
(vii) Table of readings
S/N
A / cm
B / cm
1
10.0
54.0
2
15.0
55.0
3
20.0
56.0
4
25.0
57.0
5
30.0
57.0
6
35.0
58.0
(viii) Graph of B against A
B is plotted on the vertical axis against A on the horizontal axis and the best straight line is drawn through the points.
B against A: best straight line has slope s = 0.2 and vertical-axis intercept c = 53.0 cm.
(ix) Slope, s
Using two widely-spaced points on the best line, \((A_1,B_1)=(0,\,53.0)\) and \((A_2,B_2)=(30.0,\,59.0)\):
The rule was made to balance exactly horizontal on the knife-edge before each reading of B was taken.
Error due to parallax was avoided by reading the metre rule with the eye placed vertically above the mark being read.
(b)(i) Moment of a force about a point
The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force. Its unit is the newton-metre (N m).
(b)(ii) Two conditions for equilibrium under non-parallel coplanar forces
The vector sum of all the forces is zero (i.e. the algebraic sum of their resolved components in any given direction is zero).
The algebraic sum of the moments of the forces about any point is zero.
