These rocks will be set up like this as an ornament in a Zen garden. There are f

Question

These rocks will be set up like this as an ornament in a Zen garden.

There are four rocks on a lightweight (massless) plank, which teeters on an aluminum cylinder. Here are the relevant specs:

mpile = 0.500 kg, the combined mass of all three rocks on the right

msing = 0.150 kg, the mass of the single rock on the left.

rpile = 0.350 m, the distance from the fulcrum to the pile

Determine the distance from the fulcrum to the single rock that would be necessary to ensure rotational equilibrium in the ornament. (The drawing is not to scale.)

rsingle =  m

The aluminum support cylinder, which is the fulcrum, can only support 8 N of force.

Will the cylinder be able to withstand the load? (Click to select)YesNoThere is no way to tell.

Explanation / Answer

for rotational equilibrium net torque on plank must be zero.

Apply, net torque on plank about fulcrum = 0

m_pile*g*r_pile - m_sing*g*r_sing = 0

r_sing = m_pile*r_pile/m_sing

= 0.5*0.35/0.15

= 1.167 m <<<<<<<<<-------------------Answer

Net force acting on cyllinder = m_pile*g + m_sing*g

= 0.5*9.8 + 0.15*9.8

= 6.37 N < 8 N

so, Yes. The cylinder be able to withstand the load. <<<<<<<<<-------------------Answer

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