You have landed on an unknown planet, Newtonia, and want to know what objects weigh there. When you push a certain tool, starting from rest, on a frictionless horizontal surface with a 12.0-N force, the tool moves 16.0 m in the first 2.00 s. You next observe that if you release this tool from rest at 10.0 m above the ground, it takes 2.58 s to reach the ground. What does the tool weigh on Newtonia, and what does it weigh on Earth?

Respuesta :

Answer:

Explanation:

Given

Force applied [tex]F=12\ N[/tex]

time taken [tex]t_1=2\ s[/tex]

Displacement [tex]s=16\ m[/tex]

using

[tex]s=ut+\frac{1}{2}at^2[/tex]

u=initial velocity

s=displacement

t=time

[tex]16=0+\frac{1}{2}a(2)^2[/tex]

[tex]a=8\ m/s^2[/tex]

thus mass of body [tex]m=\frac{F}{a}=\frac{12}{8}=1.5\ kg[/tex]

Next it is released from a height of [tex]h=10\ m[/tex]

time taken to reach ground [tex]t_2=2.58\ s[/tex]

using  [tex]s=ut+\frac{1}{2}at^2[/tex] in vertical direction

here acceleration is due to acceleration due to gravity(g') of the planet

as it at rest so u=0 here

[tex]10=0+\frac{1}{2}(g')(2.58)^2[/tex]

[tex]g'=3.004\ m/s^2[/tex]

Thus acceleration due to gravity on Newtonian is [tex]3\ m/s^2[/tex]

Weight of tool on Newtonia [tex]W'=mg'[/tex]

[tex]W'=1.5\times 3.004=4.506\ N[/tex]

Weight on Earth [tex]W=1.5\times 9.8=14.7\ N[/tex]