Answer
(a) $72N$
(b) $1.4m/s^2$
Work Step by Step
(a) We can find the required weight as
$F=mg+ma$
$\implies 82=mg+ma$.......eq(1)
Similarly $92=mg+2ma$.......eq(2)
Subtracting eq(1) from eq(2), we obtain:
$10=ma$
Now we plug in $ma=10$ in eq(1) to obtain:
$82=mg+10$
$\implies mg=72N$
(b) We know that
$mg=72N$
$\implies m=\frac{72N}{9.8m/s^2}$
$m=7.346Kg$
As $ma=10N$
$\implies a=\frac{10N}{m}$
We plug in the known values to obtain:
$a=\frac{10N}{7.346kg}$
$a=1.4m/s^2$
