1B7 :  Mass, Weight and Gravitational Acceleration: Keebos and Tweeks  5 pts 

In the future, we may encounter a civilization from another planet. They will not use the SI or AE systems of units. Suppose we meet aliens who use the Zerf as a unit of mass and the Spund as a unit of force.  
One Spund is the weight of a mass
of one Zerf on the
surface of Mars. The gravitational acceleration on Mars is 3.7
m/s^{2}. a.) What is g_{c} in the alien system of units? Be sure to include the numerical value and the units. 

b.) How much would a 350 Zerf object weigh on the surface of Mars, in Spunds? c.) How much would a 350 Zerf object weigh on the surface of the Earth, in Spunds? 

d.) To which system of units is the ZerfSpund system most similar, SI or AE?  
Read:  1 Zerf exerts 1 Spund of force when a = 3.7 m/s^{2}.  
The key here is that Newton's 2nd Law of Motion applies regardless of where the system is located or what system of units is used.  
Given:  a_{moon}  3.7  m/s^{2}  
m  350  Zerf  
Find:  a.)  g_{c}  ???  mZerf/Spunds^{2}  
b.)  F_{wt}  ???  Spund  for  m_{Mars}  350  Zerf  
c.)  F_{wt}  ???  Spund  for  m_{Earth}  350  Zerf  
d.)  Is this ZS system similer to the SI or AE system?  
Assumptions:  1 The acceleration of gravity at the surfae of the Earth is:  a_{Earth}  9.8066  m/s^{2}  
Equations / Data / Solve:  
Newton's 2nd Law : 

Eqn 1  
Part a.)  Solve Newton's 2nd Law for g_{c} : 

Eqn 2  


g_{c}  3.70  mZerf/Spunds^{2}  
Part b.)  Solve Newton's 2nd Law for F : 

Eqn 3  


F_{wt}  350  Spund  
Part c.)  Solve Newton's 2nd Law for F : 

Eqn 4  


F_{wt}  928  Spund  
There are two important points to this problem:  
1  The value of g_{c} is the same everywhere in the universe.  
2  If a person weighs a certain amount more on the Earth than on Mars in one system of units, then he or she also weighs proportionally more on the Earth than on Mars in any other sytem of units as well !  
Part d.)  The ZerfSpund system of units is analogous to the American Engineering System of units because g_{c} is not equal to 1 and 1 unit of mass exerts 1 unit of force (on the Mars).  
Answers:  a.)  g_{c}  3.70  mZerf/Spunds^{2}  
b.)  F_{wt}  350  Spund  
c.)  F_{wt}  930  Spund  
d.)  AE 