Final answer:
The magnitude of the downward force is 14 N.
Step-by-step explanation:
In this problem, we can use the principle of moments to find the magnitude of the downward force. The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments. Since the system is in equilibrium, the sum of the moments must be zero.
We can calculate the moments of the two objects by multiplying their masses by their respective distances from the fulcrum. For the first object with a mass of 4 kg and a distance of 28 cm, the moment is (4 kg)(28 cm). For the second object with a mass of 12 kg and a distance of 7 cm, the moment is (12 kg)(7 cm).
The downward force has a moment of its own, which is calculated by multiplying its magnitude by its distance from the fulcrum. Let's call this magnitude F. The moment of the downward force is (F)(14 cm).
According to the principle of moments, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments:
(4 kg)(28 cm) + (12 kg)(7 cm) = (F)(14 cm)
Simplifying the equation, we get:
112 cm + 84 cm = 14F cm
196 cm = 14F cm
Dividing both sides by 14 cm, we find:
F = 14 N
Therefore, the magnitude of the downward force is 14 N.