Question

A bucket of water is accelerated upward at $2.4g$. What is the buoyant force on a $3.0kg$ granite rock $(SG=2.7)$ submerged in the water? Will the rock float? Why or why not?

Answer 1

Now, We evalute normal force $N$ between rock and bucket if it comes out to be positive then rock will not float otherwise it will float.

Forces on Rock(Mass: $M$):

Buoyancy$\left(B\right)$ upward

Weight$\left(Mg\right)$ downward

Normal force$\left(N\right)$ upward

Force on displaced water(same volume as rock and mass $m$):

Buoyancy $\left(B\right)$ upward

Weight $\left(mg\right)$ downward

Now, $B+N-Mg=Ma$

$B-mg=ma$

So, $B=M(g+a)-N$ --(i)

$B=m(g+a)$

So, $M(g+a)-N=m(g+a)$

$N=(M-m)(g+a)$

Now, $m=\frac{M{\rho }_w}{{\rho }_r}$

$\therefore N=M(g+a)(1-\frac{{\rho }_w}{{\rho }_r})=3\times 3.4g\times (1-\frac{1}{2.7})$

$or,N=64.2$

So, it will not float

Now, from(i)

$B=3\times 3.4g-64.2$ = 37.8N$