Omg i really dont get this

a) show that the downward force f exerted by the clamp on the loaded cage is about 6*10^4n [4 marks]

b) calculate the initial acceleration of the loaded cage when the clamp is released [2 marks]

The sum of the forces acting on a body in equilibrium is zero

(a) The downward force exerted by the clamp, F = - W is approximately 6.0 × 10⁴ N

(b) The initial acceleration of the loaded cage is approximately 48.128 m/s²

The process of arriving at the above values is as follows:

Known parameters;

The number of elastic ropes = 2

Tension in each elastic rope before release, T = 3.7 × 10⁴ N

Angle each rope makes with the vertical tower, θ = 20°

Total mass of the loaded cage, M = 1.2 × 10³ kg

The required parameter;

(a) To show that the downward force F exerted by the clamp is about 6 × 10⁴ N

Method;

Calculate the resultant force exerted by the clamp

Solution;

The upward forces due to the elastic rope, = 2 × T × cos(θ)

∴ = 2 × 3.7 × 10⁴ × cos(20°) ≈ 69,537.25 N

The downward force due to the weight of the loaded mass, W = M × g

∴ W = 1.2 × 10³ kg × 9.82 m/s² = 11,784 N

The downward force F exerted by the clamp on the loaded cage, F, is given as follows;

F = - W

∴ F = 69,537.25 N - 11,784 N = 57,753.25 N = 5.775325 × 10⁴ N ≈ 6.0 × 10⁴ N

The downward force F exerted by the clamp, F ≈ 6.0 × 10⁴ N

b) Required; The initial acceleration of the loaded cage

Method;

Newton's third law of motion, Force, F = Mass, M × Acceleration, a,  can be applied

Solution;

Acceleration, a = F/M

The force acting on the loaded cage when the clamp is released is given by the downward force exerted by the clamp, F = 5.775325 × 10⁴ N

The acceleration of the loaded cage of mass, 1.2 × 10³ kg, is therefore;

The initial acceleration of the loaded cage when the clamp is released, a ≈ 48.128 m/s²

Learn more about equilibrium of forces here;

link

Explanation:

a) To find the downward reaction force on the clamp, we simply sum the forces in the y direction.

∑F = ma

2T cos θ − F = 0

F = 2T cos θ

F = 2 (3.7×10⁴ N) (cos 20°)

F ≈ 7.0×10⁴ N

b) Sum the forces in the y direction again, only this time, there's no downward reaction force, and the acceleration isn't 0.

∑F = ma

2T cos θ = ma

a = (2T cos θ) / m

a = (7.0×10⁴ N) / (1.2×10³ kg)

a ≈ 58 m/s²

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