Edexcel IGCSE Physics 复习笔记 1.4.2 The Principle of Moments

• The principle of moments states that:

If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot

• Remember that the moment = force × distance from a pivot
• The forces should be perpendicular to the distance from the pivot
  • For example, on a horizontal beam, the forces which will cause a moment are those directed upwards or downwards

   

Moments on a balanced beam

• In the above diagram:
  • Force F₂ is supplying a clockwise moment;
  • Forces F₁ and F₃ are supplying anticlockwise moments

   

• Due to the principle of moments, if the beam is balanced

Total clockwise moments = Total anticlockwise moments

• Hence:

F₂ × d₂ = (F₁ × d₁) + (F₃ × d₃)

Step 1: List the know quantities

• • Clockwise force (child), F_child = 140 N
  • Anticlockwise force (adult), F_adult = 690 N
  • Distance of adult from the pivot, d_adult = 0.3 m

   

Step 2: Write down the relevant equation

Moment = force × distance from pivot

• • For the see-saw to balance, the principle of moments states that

   

Total clockwise moments = Total anticlockwise moments

Step 3: Calculate the total clockwise moments

• • The clockwise moment is from the child

   

Moment_child = F_child × d_child = 140 × d_child

Step 4: Calculate the total anticlockwise moments

• • The anticlockwise moment is from the adult

   

Moment_adult = F_adult × d_adult = 690 × 0.3 = 207 Nm

Step 5: Substitute into the principle of moments equation

140 × d_child = 207

Step 6: Rearrange for the distance of the child from the pivot

d_child = 207 ÷ 140 = 1.48 m

• A light beam is one that can be treated as though it has no mass
• The supports, therefore, must supply upwards forces that balance the weight of any object placed on the beam

F₁ and F₂ upwards balance the weight of the beam downwards

• As the mass in the above diagram is moved from the left-hand side to the right-hand side of the beam, force F₁ will decrease and force F₂ will increase

F₁ decreases F₂ increases keep the beam balanced

• Consider what would happen to the beam if the right-hand support was removed:
  • Force F₂ would be 0
  • The weight of the object would supply a moment about the left-hand support, causing the beam to pivot in a clockwise direction

   

When F₂ is removed the beam will rotate by the clockwise moment

• Therefore, the force F₂ must therefore supply an anticlockwise moment about the left-hand support, which balances the moment supplied by the object

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