1m long spade balances in a string loop when the loop is 30 cm from the end of the blade. A 2 kg mass is placed at the handle and the balance point is the centre of the spade. What is the mass of the spade?

1
by charlotteds9

2015-01-25T03:34:20+05:30

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Mass of blade = m kg.  Mass of handle is M. kg  Mass of spade = M+m. kg

We balance the moments of mass/weights, using products of arm lengths to the centers of masses and masses.

from the top figure,

[ (30/L)m ] * 15 = [(L-30)/L * m ] * (L-30)/2 + M * (20 + L/2)
900*m  = m (L-30)² + M *(40+L) L
60 m =  40 M  + (m+M) L    --- (1 )

from the next diagram, we get:

(50 - L/2) m + (50-L)/2 * [(50-L)*M/(100-L)] = 2 *50 + 25 * [ 50*M/(100-L) ]

so we get,
(100-L) [100 m - L m - 200 ] = M (100 -L ) L
100 m = 200 + (m+M) L
using --(1) we get
100 m = 200 + 60 m -40 M
40 (M+m) = 200
M+m = total weight of spade  = 200/40 =  5 kg