Question

You are on the surface of an unknown planet and you wish to know what objects weigh here. When you push a small box sitting on a frictionless surface in the horizontal direction with a force of F = 10.0 N, it moves 20.0 m in the first 2.0 s. Next, you release the box from rest from a distance of 10.0 m off the ground and it takes 2.50 seconds to reach the ground. What does the box weigh on the unknown planet?

Answer 1

Gravitational acceleration on the unknown planet = g

Mass of the box = m

First you push the box along a friction less surface with a force of 10 N

Force applied on the box = F = 10 N

Acceleration of the box = a

Distance traveled by the block in 2 sec = D = 20 m

Time period = T₁ = 2 sec

Initial velocity of the box = V₁ = 0 m/s

D = V₁T₁ + aT₁²/2

20 = (0)(2) + a(2)²/2

a = 10 m/s²

F = ma

10 = m(10)

m = 1 kg

Now you release the box from a height of 10 m.

Initial velocity of the box = V₂ = 0 m/s

Distance through which the box falls = H = 10 m

Time taken for the box to reach the ground = T₂ = 2.5 sec

H = V₂T₂ + gT₂²/2

10 = (0)(2.5) + g(2.5)²/2

g = 3.2 m/s²

Weight of the box on the unknown planet = W

W = mg

W = (1)(3.2)

W = 3.2 N

Weight of the box on the unknown planet = 3.2 N