• 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

轉載自savemyexam