Question

17) A woman has a mass of 55kg.

Part A

What is her weight while standing on earth?

Express your answer to two significant figures and include the appropriate units.

       wEarth =      

Part B

What is her mass on the moon, where g=1.62m/s2 ?

Express your answer as an integer and include the appropriate units.

       mMoon =      

Part C

What is her weight on the moon?

Express your answer to two significant figures and include the appropriate units.

       wMoon =      

Answer 1

Concepts and reason

The question is based upon the concepts of gravitation.

Initially, calculate the weight of the object by multiplying the mass and the acceleration due to gravity. The mass of any body does not change with the place, it remains constant. Finally, the weight of the object on the moon is determined by computing the product of mass and the acceleration due to gravity on the moon.

Fundamentals

The weight of any body is the force by which the planet pulls the object towards itself due to the gravity. The mass and the radius of each heavenly body is different from each other which results in different values of acceleration due to gravity at different planets. The weight of the body is given by the formula:

$W = mg$ …… (1)

Here, W is the weight of the body, m is the mass of the body, and g is the acceleration due to gravity.

The mass of the body is its intrinsic property and does not change until the mass starts to travel with velocities comparable to that of the speed of light. In classical mechanics, the mass remains constant everywhere.

(A)

The weight of the woman on earth is determined as follows:

Substitute $55{\rm{ kg}}$for m and $9.8{\rm{ m/}}{{\rm{s}}^2}$for g in equation (1),

$\begin{array}{c}\\W = \left( {55{\rm{ kg}}} \right)\left( {9.8{\rm{ m/}}{{\rm{s}}^2}} \right){\rm{ N}}\\\\ = {\rm{539 N}}\\\end{array}$

(B)

The mass of the woman on the moon will be equal to that on earth. This is because the mass of the body is its intrinsic property and remains change irrespective of the acceleration due to gravity.

(C)

The weight of the woman on the moon is determined as follows:

Substitute $55{\rm{ kg}}$for m and $1.62{\rm{ m/}}{{\rm{s}}^2}$for g in equation (1),

$\begin{array}{c}\\W = 55\left( {1.62} \right){\rm{ N}}\\\\{\rm{ = 89}}{\rm{.1 N}}\\\end{array}$

Ans: Part A

The weight of the woman on earth is $539{\rm{ N}}$.

Part B

The mass of the woman on the moon is $55{\rm{ kg}}$.

Part C

The weight of the woman on the moon is $89.1{\rm{ N}}$.