A uniform half meter rule is freely pivoted at the 15cm mark and balances horizontally when a body of mass 80g is hung at the 4cm mark a.make a clear sketch to show the forces and their positions in the arrangement b.calculate the mass of the half meter rule
a. To create a clear sketch showing the forces and their positions in the arrangement, we first need to identify the forces at play.
There are three forces acting on the half meter rule: the weight of the rule acting downwards at its center of mass, the weight of the 80g body acting downwards at the 4cm mark, and the pivot force acting upwards at the 15cm mark.
The sketch would show the following forces and their positions:
- The weight of the half meter rule acting downwards at the center of mass
- The weight of the 80g body acting downwards at the 4cm mark
- The pivot force acting upwards at the 15cm mark
b. To calculate the mass of the half meter rule, we can use the principle of moments.
Taking moments about the pivot point at the 15cm mark:
Clockwise moments = Anti-clockwise moments
Weight of half meter rule * Distance from pivot = Weight of 80g body * Distance from pivot
(mass of half meter rule * g * L/2) = (80g * g * 11cm)
Solving for the mass of the half meter rule:
mass of half meter rule = (80g * 11cm) / (L/2)
Substituting L = 50cm:
mass of half meter rule = (80g * 11cm) / (50cm/2)
mass of half meter rule = 17.6g
Therefore, the mass of the half meter rule is 17.6g.