Question

A 25kg wooden plate is held in place by two strings attached to the ceiling and
the wall. The string attached to the ceiling makes an angle 40degrees with the
horizontal and the string attached to the wall makes 90degrees with the wall. Determine
the force in each string.

Answer 1

Answer:

Force in string attached to the wall is 0 newton, and force in the atring attached to the ceiling is 326newton

Answer 2

Answer:

The force in the string attached to ceiling is 157.483 Newton.

The tension of string attached with wall is 120.639 Newton.

Explanation:

Mass of wooden plate (m) = 25 kg

Gravitational acceleration (g) = 9.8 m/sec^2

So weight of wooden plate:

w = mg = 245 Newton .

String attached to the ceiling making angle = 40°

String attached to the wall making angle = 90°

Now we will divide this w = mg into Horizontal and Vertical Components.

According to the figure provided as attachment;

The Horizontal component of mg is equal with the tension of string attached to ceiling .

So,

$T1 = mg \cos(90 - 40) \degree \\ T1 = 245 \times \cos(50) \degree \\ = 157.483 \: newton$

So the force in the string attached to ceiling is 157.483 Newton .

And the Vertical Component of mg is equal with the tension of the imaginary wire (OP in figure) that is inclined with the wall.

$(T)op \: = mg \sin(50 \degree)$

The inclination of imaginary wire (OP) is also 40° with the wall.

The horizontal component of the (T)op is equal with the tension of string attached with wall:

$T2 = (T)op \: \cos(50 \degree) \\ = (mg \sin50 \degree ) \cos50 \degree \\ = 245 \times \sin50 \degree \times \cos50 \degree \\ = 120.639 \: newton$

So the tension of string attached with wall is 120.639 Newton .