Question

HELP ME

Assume a person has a mass of 50.0kg and the Earth has a mass of 5.98 x 10^24kg. If the radius of Earth is given by 6.38 x 10^6m.

a) find the gravitational force between the person and Earth

b) Find the weight of the person

c) how do these answers compare?

Answer 1

a) F =489.95 N

b) W = 490 N

c) both have same value

Step-by-step explanation:

a)

The force of gravitation between two objects is given by Newton's Law of Gravitation. According to this law:

`F = (Gm_(1)m_(2))/(r^(2))\\`

where,

F = Gravitational Force between the person and Earth = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ Nm²/kg²

m₁ = mass of peerson = 50 kg

m₂ = mass of earth = 5.98 x 10²⁴ kg

r = distance between person and earth = radius of earth = 6.38 x 10⁶ m

Therefore,

`F = ((6.67\ x\ 10^(-11)\ Nm^(2)/kg^(2))(50\ kg)(5.98\ x\ 10^(24)\ kg))/((6.38\ x\ 10^(6)\ m)^(2))\\\\`

F = 489.95 N

b)

The weight of the person will be given as:

`W = m_(1)g\\W = (50\ kg)(9.8\ m/s^(2))`

W = 490 N

c)

Both have same value