Question

ДАЮ 60 БАЛЛОВ!!!
Determine the forces in cables AC and AB needed to hold the 20-kg ball D in equilibrium.Take F = 300 N and d = 1 m.​

Answer 1

Ответ:

To determine the forces in cables AC and AB needed to hold the 20-kg ball D in equilibrium, we can use the principles of equilibrium. The forces in cables AC and AB must balance the weight of the ball, which is equal to the mass (20 kg) times the acceleration due to gravity (approximately 9.81 m/s²).

The force of gravity (weight) acting on the ball D is given by:

Weight = mass × gravity

Weight = 20 kg × 9.81 m/s²

Weight ≈ 196.2 N

Now, let's consider the forces in the cables:

1. Cable AC: Since cable AC is at an angle θ to the vertical, we can resolve it into two components:

- A vertical component (AC_v) that opposes the weight of the ball.

- A horizontal component (AC_h) that has to balance the horizontal force (F).

2. Cable AB: Cable AB is purely vertical and must counteract the vertical component of the ball's weight.

To find the components of force in cable AC, we can use trigonometry. The angle θ is given by:

θ = tan⁻¹(d / (2 * F))

θ = tan⁻¹(1 m / (2 * 300 N))

θ ≈ 1.19 degrees

Now, we can find the vertical and horizontal components of cable AC:

- AC_v = 196.2 N (to balance the weight of the ball)

- AC_h = F (to balance the horizontal force)

For cable AB, it needs to counteract the vertical component of the ball's weight:

- AB = 196.2 N

So, the forces in cables AC and AB needed to hold the ball in equilibrium are approximately:

- AC_v ≈ 196.2 N

- AC_h ≈ 300 N

- AB ≈ 196.2 N