Question

1. a woman has a mass of 55 kg on earth.

a. what is the woman’s mass on the moon?
b. what would be the woman’s weight on the moon where the acceleration due to gravity is 1.67 m/s²? calculate the weight in both newtons and pounds.

1. a man has a mass of 80 kg on earth.

a. what is the man’s weight on earth in newtons? what is the man’s weight on earth in pounds?
b. what is the man’s weight on mars where the acceleration due to gravity is 3.7 m/s²? show your answer in both newtons and pounds.
c. what is the man’s mass while on mars? explain your answer.

Explanation:

Step1: Calculate weight on Earth

Weight \(W = mg\), where \(m = 80\space kg\) and \(g_{Earth}=9.8\space m/s^{2}\).
\(W_{Earth}=80\times9.8 = 784\space N\)
To convert Newtons to pounds, use the conversion factor \(1\space N=0.224809\space lb\).
\(W_{Earth\space(lb)}=784\times0.224809\approx176.25\space lb\)

Step2: Calculate weight on Mars

Given \(g_{Mars} = 3.7\space m/s^{2}\)
\(W_{Mars}=80\times3.7=296\space N\)
\(W_{Mars\space(lb)}=296\times0.224809\approx66.54\space lb\)

Step3: Mass on Mars

Mass is an intrinsic property of an object and does not depend on the gravitational field. So, \(m_{Mars}=80\space kg\)

Answer:

a. \(784\space N\), \(176.25\space lb\)
b. \(296\space N\), \(66.54\space lb\)
c. \(80\space kg\) (Mass is independent of location)