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Chapter 1: Q43P (page 360)

A box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank. The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is 50.0 cm from the right end. What mass of sand should be put into the box so that the plank balances horizontally on a fulcrum placed just below its midpoint?

Short Answer

Expert verified

The mass of sand is 20 kg.

Step by step solution

01

The given data

Given that a box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank.

The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it.

The center of gravity of the nonuniform plank is 50.0 cm from the right end.

02

Formula used

Center of mass, x=m1x1+m2x2m1+m2where

m1and m2are masses of the system and x1,andx2are positions of masses.

03

Find the mass of the sand

Let the fulcrum be the origin.

Let m1=25kg

So x1=0.5m

Let m2be mass of the sand

So x2=-0.625m

Since the center of gravity is in the middle of the box

Therefore x = 0 m

This implies x=m1x1+m2x2m1+m2= 0 m

Thus

(25kg)(0.5m)+m2(鈭�0.625m)m1+m2=0mm2=12.5m鈰�kg0.625mm2=20kg

Hence, the mass of sand required is 20 kg.

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