Question

3) A large cubic concrete block that is 50 cm on a side is submerged in water and rests on a rubber mat. The coefficient of kinetic friction between the concrete and the rubber surface is 0.5.

A team of divers under the water pull on the block with a total horizontal force of 950 N. Determine the instantaneous acceleration of the concrete block. Assume that the drag force of the fluid acting on the block as it moves is not significant until the block reaches significant speed, so it can be ignored for this question. (Density = 2.3x10^3 kg/m^3)

Answer 1

here,

the density of water , p1 = 1000 kg/m^3

the density of block , p2 = 2300 kg/m^3

the side of large cube , a = 50 cm

a = 0.5 m

the normal force , N = (m * g - p1 * V * g)

N = ((V * p2) * g - p1 * V * g)

the coefficient of kinetic friction , uk = 0.5

the horizontal force , F = 950 N

the instantaneous acceleration , a = net force /effective mass

a = (F - uk * N)/m

a = (F - uk * ((V * p2) * g - p1 * V * g) ) /(p2 * V)

a = (950 - 0.5 * ((0.5^3 * 2300) * 9.81 - 1000 * 0.5^3 * 9.81) ) /(2300 * 0.5^3) m/s^2

a = 0.53 m/s^2