(1) A metre rule balances when the 50 cm mark is directly above a pivot.
(a) State where in the rule its centre of mass is located.
(b) Fig. 3.1 shows an apple and a 0.40 N weight placed on the rule so that the rule remains balanced at the 50 cm mark.
The centre of mass of the apple is 25 cm from the pivot and the centre of mass of the weight is 45 cm from the pivot.
Calculate
(i) the weight of the apple
(ii) the mass of the apple.
(c) The apple is not moved. The weight is removed from the rule and the pivot is moved to the left until the rule balances as shown in Fig. 3.2.
(i) Explain why the arrangement in Fig. 3.2 balances.
(ii) The pivot in Fig. 3.2 is closer to the 50 cm mark than to the centre of mass of the apple.Compare the weight of the rule to the weight of the apple.
Answers
Answer:
The middle or centre is the location in the rule where the centre of mass is located and the weight of the apple is 0.72N while its mass is 7.2 N. The arrangement balances the rule because it does not have enough weight on its right, the pivot is relocated to the left in order to balance the rule. When the pivot is closer to the 50 cm mark than to the centre of mass of the apple, the weight is carried by the apple than by the ruler.
Explanation:
a) The middle or centre is the location in the rule where the centre of mass is located. A position established in relation to an object or set of objects is the centre of mass. It represents the system's average location as weighted by each component's mass. The centre of mass for straightforward stiff objects with homogeneous density is found at the centroid.
b) The weight's centre of mass is 45 cm from the pivot, whereas the apple's centre of mass is 25 cm away.
i) To calculate the weight of the apple,
Let the weight of the apple be represented as x
We know, the weight of apple × Centre of mass of the apple from the pivot = Centre of mass of the weight of the apple × Weight placed on rule
Therefore, x × 25 = 45 × 0.4
x = 0.72 N
Thus, weight of the apple is 0.72N
ii) To calculate the mass of the apple, Mass of the sample = Gravity of earth × Weight of the apple
We know, The gravity of earth = 9.8 ≈ 10
Therefore, the Mass of the apple = 10 x 0.72
Mass of the apple = 7.2 N
c) The apple is not moved. The weight is removed from the rule and the pivot is moved to the left until the rule balances:
i) The apple is not moved. The weight is removed from the rule and the pivot is moved to the left until the rule balances. This arrangement balances the rule because it does not have enough weight on its right, the pivot is relocated to the left in order to balance the rule.
ii) When the pivot is closer to the 50 cm mark than to the centre of mass of the apple, the weight is carried by the apple than by the ruler.
Thus, a) The middle or centre is the location in the rule where the centre of mass is located.
b) i) The weight of the apple is 0.72N
ii) Mass of the apple = 7.2 N
c) i) This arrangement balances the rule because it does not have enough weight on its right, the pivot is relocated to the left in order to balance the rule.
ii) When the pivot is closer to the 50 cm mark than to the centre of mass of the apple, the weight is carried by the apple than by the ruler.
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