Question

A metal bar 70 cm long and 4.00 kg in mass supported on two knife--edges placed 10 cm from each end. A 6.00 kg load is suspended at 30 cm from one end. Find the reactions at the knife-edges. (Assume the bar to be of uniform cross section and homogeneous.)

Answer 1

To find the normal reaction due to edges we will use the concept of moment of force about a point.

Since system is in equilibrium i.e. rod is balanced about edges, therefore we have

Applying equilibrium condition of moment about the point A (edge A)

Moment of normal reaction of edge B about A= Moment of rod about A$\times$ Moment of 6 kg mass about A

$N_B\times 50=4g\times 25+6g\times 20$

here $N_B$ is a normal reaction due to edge B in upward direction

$4g$ is weight of the rod in downward direction

$6g$ is weight of the mass in downward direction

therefore,

$N_B=\frac{(100+120)g}{50}=\frac{220}{50}g=\frac{22}{5}g=4.4g$

Similarly, applying equilibrium condition of moment about the point B (edge B)

We get

$N_A\times 50=4g\times 25+6g\times 30$

$N_A=\frac{(100+180)g}{50}=\frac{280}{50}g=\frac{28}{5}g=5.6g$

Therefore, normal reaction on the edges is 4.4g and 5.6g, where g is acceleration due to gravity.