**Example 1**

The diagram shows the side view of a laptop computer. A student opens the computer with an upward force of 4.2N. The force is applied 0.25m from the pivot.

(a) Calculate the moment of the force that opens the computer.

moment = force x distance = 4.2 x 0.25 = 1.05 N·m

(b) The student finds that 4.2N is the minimum upward force needed to open the computer. Then the student applies a downward force, F, to close the computer. Explain why the minimum force needed to close the computer is likely to be less than 4.2N.

The moment of weight of the laptop acts in the same direction as the force to close the computer. Therefore, it takes less force to close the laptop than to open it.

**Example 2**

A student investigates the principle of moments. He connects a ruler to a stand with a pivot. He hangs a 2N weight from the 60cm mark on the ruler. He uses a forcemeter to hold the ruler horizontal.

(a) How can the student check that the ruler is horizontal?

- Measure the height of the ruler from the ground at various locations and check that the height is same for all locations of the ruler OR
- Measure the angle between the stand and the ruler and make sure that they are perpendicular OR
- Place a spirit level on the ruler and make sure that the bubble is located in the middle

(b) Calculate the moment of the 2N weight.

moment = 2 x 0.6 = 1.2 N·m

(c) The student holds the ruler horizontal with the forcemeter at the 10cm mark. He expects the reading on the forcemeter to be 12N. Is the student correct?

- Since the ruler is held horizontal, the clockwise moment should balance the anticlockwise moment.
- Forces causing clockwise moment are 2N weight and the weight of the ruler.
- The anitclockwise moment is caused by the pulling force of the forcemeter.
- Without considering the weight of the ruler, the moment provided by the forcemeter should equal the moment of 2N weight. F x 0.1 = 1.2 → F = 12N
- However, since the forcemeter should also support the weight of ruler, the
**reading on the forcemeter should be larger than 12N**.

**Example 3**

Two fishermen uses a pole to carry some fish. Fisherman A and B feel different forces on their shoulders. Explain which fisherman feels the larger force.

- The anticlockwise moment on A and the clockwise moment on B are equal to each other since the pole is balanced.
- The fish, which acts as the pivot, is closer to fisherman A; the distance from the pivot to A is shorter than the distance from the pivot to B.
**The force acting on fisherman A is larger**.- Mathematically,

_{A}x d

_{A}= F

_{B}x d

_{B}

_{A}= F

_{B}x (d

_{B}/ d

_{A})

_{B}/ d

_{A}) > 1,

**F**

_{A}> F_{B}**Example 4**

A student can use a claw hammer to pull a nail from a piece of wood. The diagram shows two forces acting on the hammer. Suggest three ways that the student can increase the moment on the hammer.

The force that causes the moment which makes it possible to pull the nail from the wood is F_{1}.

- Increase the magnitude of F
_{1}; pull the hammer with a larger force - increase distance 1; hold the hammer as close to the end as possible or use a hammer with a longer handle
- maintain F
_{1}perpendicular to the hammer