Answer:
[tex]g_{moon}=1.67 [m/s^{2} ][/tex]
Explanation:
The weight of some mass is defined as the product of mass by gravitational acceleration. In this way using the following formula we can find the weight.
[tex]w =m*g\\[/tex]
where:
w = weight [N]
m = mass = 0.06 [kg]
g = gravity acceleration = 10 [N/kg]
Therefore:
[tex]w=0.06*10\\w=0.6[N][/tex]
By Hooke's law we know that the force in a spring can be calculated by means of the following expression.
[tex]F=W\\F = k*x[/tex]
where:
k = spring constant [N/m]
x = deformed distance = 6 [cm] = 0.06 [m]
We can find the spring constant.
[tex]k= F/x\\k=0.6/0.06\\k=10 [N/m][/tex]
Since we use the same spring on the moon and the same mass, the constant of the spring does not change, the same goes for the mass.
[tex]F_{moon}=k*0.01\\F = 10*0.01\\F=0.1[N][/tex]
Since this force is equal to the weight, we can now determine the gravitational acceleration.
[tex]F=m*g_{moon}\\g=F/m\\g = 0.1/0.06\\g_{moon} = 1.67[m/s^{2} ][/tex]
