Three objects are placed on a uniform metre rule that is balanced at the 50 cm mark. The table shows their positions and weights. Object Position on rule / ...
Question 1 Report
Three objects are placed on a uniform metre rule that is balanced at the 50 cm mark. The table shows their positions and weights.
| Object | Position on rule / cm | Weight / N |
|---|---|---|
| P | 10 | 4.0 |
| Q | 25 | 2.0 |
| R | 75 | W |
The rule is in equilibrium. What is the value of W?
Answer Details
For the rule to be in equilibrium, the total clockwise moment about the pivot must equal the total anticlockwise moment. The pivot is at the 50 cm mark.
Objects P and Q are on the left of the pivot, so they produce anticlockwise moments. Object R is on the right.
Anticlockwise moments:
- P: \( 4.0 \times (50 - 10) = 4.0 \times 40 = 160 \text{ N cm} \)
- Q: \( 2.0 \times (50 - 25) = 2.0 \times 25 = 50 \text{ N cm} \)
Total anticlockwise moment = 210 N cm.
Clockwise moment from R: \( W \times (75 - 50) = W \times 25 \)
Setting clockwise equal to anticlockwise:
\[ W \times 25 = 210 \]
\[ W = \frac{210}{25} = 8.4 \text{ N} \]
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