Question

You have landed on an unknown planet, Newtonia, and want to know what objects will weigh there. You find that when a certain tool is pushed on a frictionless horizontal surface by a 12.0 N force, it moves 16.4 m in the first 2.50 s, starting from rest. You next observe that if you release this tool from rest at 10.3 m above the ground, it takes 2.88 s to reach the ground.What does the tool weigh on Newtonia (in N)?What would it weigh on Earth (in N)?

Answer 1

Answer:

$w'=5.679\ N$ on the planet

$w=22.43\ N$ on earth

Explanation:

Given:

• initial velocity of the tool before pushing, $u=0\ m.s^{-1}$

• force applied on the tool, $F=12\ N$

• displacement of the tool, $s=16.4\ m$

• time taken for the displacement, $t=2.5\ s$

• height of releasing  the tool, $h=10.3\ m$

• time taken by the tool to fall on the ground, $t_v=2.88\ s$

Now using the equation of motion:

$s=u.t+\frac{1}{2}a.t^2$

where:

a = acceleration of the object

$16.4=0+0.5\times a\times 2.5^2$

$a=5.248\ m.s^{-2}$

Now the mass of the tool:

$m=\frac{F}{a}$

$m=\frac{12}{5.248}$

$m=2.2866\ kg$

Using the equation of motion when the tool is dropped:

$h=u.t_v+\frac{1}{2} \times g.t_v^2$

here:

g = acceleration due to gravity on the planet

$10.3=0+0.5\times a\times 2.88^2$

$g=2.4836\ m.s^{-2}$

Weight of the tool in the planet:

$w'=m.g$

$w'=2.2866\times 2.4836$

$w'=5.679\ N$

Weight of the tool on the earth:

$w=m.g'$

$w=2.2866\times 9.81$

$w=22.43\ N$

Answer 2

Answer:

Explanation:

Force, F = 12 N

distance, s = 16.4 m

time, t = 2.5 s

initial velocity, u = 0 m/s

Let a be the acceleration

use second equation of motion

s = ut + 1/2 at²

16.4 = 0 + 0.5 x a x 2.5 x 2.5

a = 5.25 m/s²

Let m be the mass of the tool.

F = ma

12 = m x 5.25

m = 2.286 kg

Now for vertical motion

h = 10.3 m

u = 0 m/s

t = 2.88 m/s²

Let the acceleration due to gravity on that planet is g'

Use second equation of motion

10.3 = 0 + 0.5 x g' x 2.88 x 2.88

g' = 2.485 m/s²

Let W' be the weight of the tool on that planet

W' = m g' = 2.286 x 2.485 = 5.68 N

Let W be the weight of the tool on the earth

W = m x g = 2.286 x 9.8 = 22.4 N