Question

Calculate the unknown forces X and Y for the balanced beam shown.

Answer 1

Given:

A balanced beam is shown.

To find:

Value of X and Y ?

Calculation:

Since the beam is in ROTATIONAL EQUILIBRIUM w.r.t to wedge point, we can say :

$\sum( \tau) = 0$

$\implies \: (X \times 1) - (400 \times 2.5) = 0$

$\implies \: X - 1000 = 0$

$\boxed{ \implies \: X = 1000 \: N}$

• The beam is also in TRANSLATIONAL EQUILIBRIUM :

$\sum(F) = 0$

$\implies \: X - Y + 400 = 0$

$\implies \: 1000 - Y + 400 = 0$

$\boxed{ \implies \:Y = 1400 \: N}$

So, value of X is 1000 N and Y is 1400 N.