Fig. 8.1 shows a horizontal beam of negligible weight supported at point P. Two forces act on the beam as shown. A 12 N upward force acts 0.50 m to the left...
Question 1 Report
Fig. 8.1 shows a horizontal beam of negligible weight supported at point P. Two forces act on the beam as shown.
A 12 N upward force acts 0.50 m to the left of P. An 8.0 N downward force acts 0.40 m to the right of P.
(a) Calculate the clockwise moment about P. [1]
(b) Calculate the anticlockwise moment about P. [1]
(c) State whether the beam is in equilibrium. Explain your answer. [2]
(d) Calculate the resultant moment about P and state its direction. [2]
Answer Details
(a) Clockwise moment about P
The 8.0 N force acts downward, 0.40 m to the right of P. Looking at the beam, this force would tend to rotate the beam clockwise about P.
\( \text{clockwise moment} = 8.0 \times 0.40 = 3.2 \text{ N m} \) [1]
(b) Anticlockwise moment about P
The 12 N force acts upward, 0.50 m to the left of P. An upward force on the left side creates an anticlockwise rotation about P.
\( \text{anticlockwise moment} = 12 \times 0.50 = 6.0 \text{ N m} \) [1]
(c) Is the beam in equilibrium?
The beam is not in equilibrium. [1]
For equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments. Here, the anticlockwise moment (6.0 N m) does not equal the clockwise moment (3.2 N m), so the condition for equilibrium is not satisfied. [1]
(d) Resultant moment about P
The resultant moment is the difference between the two moments:
\( \text{resultant moment} = 6.0 - 3.2 = 2.8 \text{ N m} \) [1]
Since the anticlockwise moment is larger, the resultant is in the anticlockwise direction. [1]
The beam will rotate anticlockwise about P until something stops it or until the forces change.
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