# Moment, equilibrium questions and answers

### 1. When is object said to be in equilibrium?

Answer: An object is said to be in equilibrium if is acted upon by two or more force and it does move or rotate. It shows that the resultant force acting on the system or the object is equal to zero.

### 2. What is moment of force about a point?

Answer:  The moment of force about a point is the products of force and the perpendicular distance from the point to the line of action of force.

### 3. While is it easier to loosen a nut with a long spanner than a short one?

Answer: It is because with a long spanner, a small force you applied can produce a very big moment, but it is not like that with a short spanner

## 4. What is a couple?

Answer:  A couple is a system of two equal and parallel but opposite force not acting along the same line. The resultant of the force is zero, but the resultant moment is not zero.

### 5. What is the resultant moment of a couple?

Answer:  The resultant moment of a couple, is the products of one of the forces and the perpendicular distance between the lines of action of the forces.

## 6. State the principle of moments

Answer: The principle of moments states that if a body is in equilibrium, the sum of the clockwise turning moment is equal to the sum of anticlockwise turning moment about the same point.

### 7. Using the diagram below find the moment of force 20N about points A and B

Answer:  h=3 x cos60 = 3 x 0.5 =1.5m

The moment of force about A =1.5 x 20 =30Nm

The moment of force about B =zero, since the distance from B is zero = zero

#### 8. What is the magnitude of a couple which act on a rotating circular disc of a radius 2m pivoted at the centre by a tangential force of 4N

Answer:  The magnitude of the couple is 2 x 4 = 8N

#### 9. A weightless bar is pivoted at its center and weights of 5N and 10N, placed 3m and 2m respectively from the pivot on one side, are balanced by a weight of 20N on the other side. How far is the 20N weight from pivot?

Using the principle of momentum, that is  the clockwise moment = the anticlockwise moment, so

CW =ACW =

20x =(5 x 3) + (10 x 2)

20x =15 + 20

20x =30

So the 20N is 1.75m away from the pivot.

### 10. What is center of gravity, and why is it that when a body is supported at the center of gravity it remains stable?

Answer: The center of gravity is defined as the point at which the weights of a body seem to act toward or concentrated.  When a body is acted upon at this point, it remain stable because that is where the weight concentrated or balanced

## 11. Define the followings:

(a).Stable equilibrium

(b). Unstable equilibrium

(c). Neutral equilibrium

Answer; (a). Stable equilibrium: A body is said to be in a stable equilibrium if it receive slight displacement and it tends to return to its original position.

(b) Unstable equilibrium: A body is said to be in an unstable equilibrium when on receiving a

Slight displacement tends to r or move further from its original position.

(c). Neutral equilibrium: A body is said to be on a neutral equilibrium if on receiving a slight

Displacement tend to remain or come to rest in its new position

#### 12.A uniform bar with weight 20N rest on two support P and Q as shown and weight are suspended as shown in diagram below. Calculate the reactions at P and Q on the support

Answer:  Considering the upwards and downwards forces which are equal and opposite to each other we have

A + Y =15 + 20 + 5 = 40……(1)

Now we take moment at either P or Q, let take moment about P though if we take moment about Q we are going to arrive at the same result at the end

Anticlockwise moment = clockwise moment, therefore

Y x 5 + 15 x 3 = 2 x 20 + 5 x 7…….(2)

5Y + 45 = 40 + 35

5Y =75 – 45 = 30

5Y = 30

Y = 6N

Using the value of Y in equation one we have

A + 6 =40

A = 40 -6 = 34

A = 36N

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