Question

The standard acceleration (at sea level and 45◦ latitude) due to gravity is 9.806 65 m/s2. What is the force needed to hold a mass of 2 kg at rest in this gravitational field? How much mass can a force of 1 N support?

Answer 1

19.613 N

0.10197 kg

Step-by-step explanation:

m = Mass of object = 2 kg

a = Acceleration due to gravity = 9.8065 m/s²

Force

`F=m(GM)/(r^2)\\\F=ma`

where

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

M = Mass of Earth = 5.972 × 10²⁴ kg

r = Radius of Earth = 6.3781×10⁶ m

⇒F = ma

⇒F = 2×9.8065

⇒F = 19.613 N

∴ Force needed to hold a mass at rest is 19.613 N.

Force = F = 1 N

F = ma

`1=m9.8065\\\Rightarrow m=(1)/(9.8065)\\\Rightarrow m=0.10197\ kg`

∴ 1 N can support 0.10197 kg of mass