Question

2. A block of wood weighs 160 N and has a specific gravity of 0.60 (density = 600 kg/m^3). How many Newtons of downward force is required to sink it in fresh water.

Answer 1

The weight of wood as follows: W = mg Calculate the mass of wood as follows: W m=- 8 160 N 9.8 m/s? = 16.32653 kg Calculate the volume of the block as follows: m V Р. 16.32653 kg 600 kg/m = 0.02721 m = The specific gravity is the ratio of density of wood to the density of water. р, v= Pw - Pw The density of water is, Po 7 600 kg/m 0.6 = 1000 kg/m² The condition for the wood to sink is specific gravity must be equal to 1 or should be greater than 1 (y'1). Let the required additional force to sink the wood is F. Hence, F = Mg

The additional mass is, F M 8 The required additional force is, y' Pó Pw — 1= po Pw Pw = PA m. "total Pw V m+M Pw w V F m +- g V F PV =m+ g F = PV-m g F =(PV-m)g - Calculate the required additional force to sink the wood as follows: F=(PV –m)g =[(1000 kg/m?)(0.02721 mº)-16.32653 kg](9.8 m/s”) = 106.658 N =110 N (rounding off to two significant figures) Thus, the additional downward force is 110 N.