Question

Course hero N4M.6 A board has one end wedged under a rock having a mass of 380 kg and is supported by another rock that touches the bottom side of the board at a point 85 cm from the end under the rock. The board is 4.5 m long, has a mass of about 22 kg, and projects essentially horizontally out over a river. Is it safe for an adult with a mass of 62 kg to stand at the unsupported end of the board

Answer 1

Therefore it is save to carry a 62kg adult

Step-by-step explanation:

From the question we are told that:

Mass
`m=380kg`

Height of supporting Rock
`X=85cm`

Length of Board
`L_r=4.5m`

Mass of board
`M_b=22kg`

Mass of adult
`M_a=62`

Generally the moment of balance about wedge part about is mathematically given by

`N -Q + R = Mg + mg`

`0.85*N - Mg*2.25 - mg*(2.25 + x) = 0`

`0.85*N = + Mg*2.25 + mg*(2.25 + x)`

where

`N+R=4547`

therefore

`N = 570.70588 + 1608.3529 + 714.823 x`

if N=0 at fallen person

`x=3.04m`

Therefore it is save to carry a 62kg adult