A spiral spring of natural 20.00cm has a scale pan hanging freely in it's lower end. When an object of mass 40g is placed in the pan,its length becomes 21.80cm.when another object of mass 60g is placed in the pan,the length becomes 22.05cm.

Question

A spiral spring of natural 20.00cm has a scale pan hanging freely in it's lower end. When an object of mass 40g is placed in the pan,its length becomes 21.80cm.when another object of mass 60g is placed in the pan,the length becomes 22.05cm.
calculate the mass of the scale pan?

oobleck · Accepted Answer

recall that the displacement is proportional to the mass. So, if the scale pan has mass m,
k(m+40) = 1.80
k(m+60) = 2.05
Now just solve for m.

These are the equations if the two weighings are done separately. If the 60g mass is added to the 40g mass, the 2nd equation needs to change...