Answer
The weight of the tool on Newtonia is 4.50 N.
The weight of the tool on Earth is 14.7 N.
Work Step by Step
We can find the acceleration of the tool as it moves on a frictionless surface.
$y = \frac{1}{2}at^2$
$a = \frac{2y}{t^2} = \frac{(2)(16.0~m)}{(2.00~s)^2}$
$a = 8.00~m/s^2$
We can use a force equation to find the mass of the tool.
$F = ma$
$m = \frac{F}{a} = \frac{12.0~N}{8.00~m/s^2}$
$m = 1.50~kg$
We can use the motion in freefall to find the acceleration due to gravity $g_N$ on Newtonia.
$y = \frac{1}{2}(g_N)t^2$
$g_N = \frac{2y}{t^2} = \frac{(2)(10.0~m)}{(2.58~s)^2}$
$g_N = 3.00~m/s^2$
The weight of the tool on Newtonia is $(m)(g_N)$.
$weight = (1.50~kg)(3.00~m/s^2) = 4.50~N$
The weight of the tool on Newtonia is 4.50 N.
The weight of the tool on Earth is $mg$.
$weight = (1.50~kg)(9.80~m/s^2) = 14.7~N$
The weight of the tool on Earth is 14.7 N.
