Question

Two unlike parallel forces are acting at a distance of 450 mm from each other. The forces are equivalent to a single force of 90 N, which acts at a distance of 200 mm from the greater of the two forces. Find the magnitude of the forces.

Answer 1

To find the magnitude of the forces, set up the equation of moments. The magnitude of the greater force is 2.25 times the magnitude of the lesser force plus 90 N. The magnitude of the lesser force is found by subtracting 90 N from the greater force and dividing by 2.25.

Step-by-step explanation:

To find the magnitude of the forces, we can set up the equation of moments. Let's consider the point where the single force of 90 N is acting. The moment of this force about this point is equal to the sum of the moments of the two parallel forces about the same point. The moment of a force is given by the product of the force and the perpendicular distance from the point to the line of action of the force.

Let's denote the magnitude of the greater force as F1 and the magnitude of the lesser force as F2. The equation of moments is:

F1 * (200 mm) = F2 * (450 mm) + 90 N * (200 mm)

Simplifying the equation, we have:

F1 = (F2 * (450 mm) + 90 N * (200 mm)) / (200 mm)

Substituting the values, we get:

F1 = (F2 * 450 + 90 * 200) / 200

F1 = (450F2 + 18000) / 200

F1 = 2.25F2 + 90

Since the forces are unlike, the magnitude of the greater force (F1) must be greater than the magnitude of the lesser force (F2). Therefore, the magnitude of the forces is F1 = 2.25F2 + 90 N and F2 = (F1 - 90) / 2.25 N.

Answer 2

Using the principle of moments, the magnitude of the two unlike forces was determined to be 50 N for the larger force and 40 N for the smaller force.

Step-by-step explanation:

To solve this question, we will apply the principle of moments, which states that for a system to be in equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments about any point. Given that two unlike parallel forces are acting at a distance of 450 mm from each other and are equivalent to a single force of 90 N, this resultant force acts at a distance of 200 mm from the greater of the two forces.

Let F1 be the greater force and F2 be the smaller force. The moments about the point of action of the smaller force (anticlockwise moment) is F1 × 450 mm and the moments about the same point (clockwise moment) is 90 N × 250 mm because the resultant 90 N force is 200 mm from the larger force, adding 50 mm to the distance between the forces. By equating the moments:

F1 × 450 = 90 × 250

Dividing both sides by 450 gives:

F1 = (90 × 250) / 450

F1 = 50 N

Since the two forces are unlike but equivalent to a single force of 90 N, the other force can be found by subtracting this from 90 N:

F2 = 90 N - 50 N

F2 = 40 N

Therefore, the magnitudes of the forces are 50 N and 40 N.