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Fig below shows a mass suspended by wire strops from fixed points A and B. Determine the force in strop AC and the force in strop BC.

Physics

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2 parts
b(i)

2824.4 N\text{2824.4 N}

b(ii)

4264.1 N\text{4264.1 N}

Step-by-step solution

3 steps

a) Equilibrium is a state where an object experiences no net force and no net torque. This means the object is either at rest (static equilibrium) or moving with a constant velocity (dynamic equilibrium).

Part b· 3 steps

  1. Calculate the weight of the suspended mass.

    The mass m=500 kgm = 500 \, \text{kg}.
    The acceleration due to gravity g=9.81 m/s2g = 9.81 \, \text{m/s}^2.
    The weight WW is given by:

    W=m×g=500 kg×9.81 m/s2=4905 NW = m \times g = 500 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 4905 \, \text{N}
  2. Identify the angles for Lami's Theorem.

    Let T1T_1 be the force in strop AC and T2T_2 be the force in strop BC. The weight WW acts vertically downwards.
    The angles are measured between the lines of action of the forces:

    • Angle between T1T_1 (strop AC) and T2T_2 (strop BC) is given as 95∘95^\circ.
    • Angle between T1T_1 (strop AC) and WW (vertical downward force): Strop AC makes an angle of 30∘30^\circ with the horizontal. The vertical force WW is 90∘90^\circ from the horizontal. So, the angle between T1T_1 and WW is 30∘+90∘=120∘30^\circ + 90^\circ = 120^\circ.
    • Angle between T2T_2 (strop BC) and WW (vertical downward force): Strop BC makes an angle of 55∘55^\circ with the horizontal. The vertical force WW is 90∘90^\circ from the horizontal. So, the angle between T2T_2 and WW is 55∘+90∘=145∘55^\circ + 90^\circ = 145^\circ.
  3. Apply Lami's Theorem.

    Lami's Theorem states that for three forces in equilibrium, each force is proportional to the sine of the angle between the other two forces.

    T1sin⁡(145∘)=T2sin⁡(120∘)=Wsin⁡(95∘)\frac{T_1}{\sin(145^\circ)} = \frac{T_2}{\sin(120^\circ)} = \frac{W}{\sin(95^\circ)}

Part b(i)

2824.4 N\text{2824.4 N}

Determine the force in strop AC (T1T_1).

Using the relation for T1T_1:

T1=Wsin⁡(145∘)sin⁡(95∘)T_1 = W \frac{\sin(145^\circ)}{\sin(95^\circ)} T1=4905 N×sin⁡(35∘)sin⁡(95∘)T_1 = 4905 \, \text{N} \times \frac{\sin(35^\circ)}{\sin(95^\circ)} T1=4905 N×0.5735760.996195T_1 = 4905 \, \text{N} \times \frac{0.573576}{0.996195} T1≈4905 N×0.57576T_1 \approx 4905 \, \text{N} \times 0.57576 T1≈2824.4 NT_1 \approx 2824.4 \, \text{N}

The force in strop AC is 2824.4 N\boxed{\text{2824.4 N}}.

Part b(ii)

4264.1 N\text{4264.1 N}

Determine the force in strop BC (T2T_2).

Using the relation for T2T_2:

T2=Wsin⁡(120∘)sin⁡(95∘)T_2 = W \frac{\sin(120^\circ)}{\sin(95^\circ)} T2=4905 N×sin⁡(60∘)sin⁡(95∘)T_2 = 4905 \, \text{N} \times \frac{\sin(60^\circ)}{\sin(95^\circ)} T2=4905 N×0.8660250.996195T_2 = 4905 \, \text{N} \times \frac{0.866025}{0.996195} T2≈4905 N×0.86933T_2 \approx 4905 \, \text{N} \times 0.86933 T2≈4264.1 NT_2 \approx 4264.1 \, \text{N}

The force in strop BC is 4264.1 N\boxed{\text{4264.1 N}}.

2 हो गए। आज 3 बाकी — अगला भेजो।

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