Answer
(a) $1.274N$
(b) $7.92m/s$
(c) Please see the work below.
Work Step by Step
(a) We can find the magnitude of the force of gravity as
$W=mg$
We plug in the known values to obtain:
$W=(0.13Kg)(9.81m/s^2)$
$W=1.274N$
(b) We know that
$v^2=v_{\circ}^2+2g\Delta y$
$\implies v^2=0+2g\Delta y$
$\implies v=\sqrt{2g\Delta y}$
We plug in the known values to obtain:
$v=\sqrt{2(9.8)(3.2)}$
$v=7.92m/s$
(c) We know that
$F=mgh$
We plug in the known values to obtain:
$F=(0.13)(9.8)(3.2)$
$F=4.077Kgm^2/s^2$
Now $\frac{1}{2}mv^2=\frac{1}{2}(0.13)(7.92)^2$
$\frac{1}{2}m(v)^2=4.077Kgm^2/s^2$
Thus $mgh=\frac{1}{2}mv^2$
The dimensions of the above both equations are $\frac{ML^2}{T^2}.$
