Example of properties of matter
Example: A five metre long steel wire is suspended from the ceiling. A sphere of mass 25 kg and 10 cm radius is attached to another end of the wire. The height of the ceiling is 5.21 m. When the sphere is made to oscillate as a pendulum, then its lowest point just touches the floor. Find the velocity of the sphere at the lowest point. Given Y=2×1011 N m-2 and radius of wire = 0.05 cm.
Solution: Here, l = 5m; m=25kg; R =10 cm;
R= 0.05 cm= 0.05 × 10-2 m =5 × 10-4 m;
Y = 2 × 1011 Nm-2
The distance between lowest point of the sphere to the point of suspension of wire =5 +20 × 10-2
= 5.20 m
When the sphere oscillates as pendulum, it just touches to the floor, therefore extension in wire,
Δl= 5.21 – 5.20=0.01 m
Thus stretching force F = AY Δl/l = πr2Y Δl/l
The force acting on the wire at the lowest point is :
F = mg + mv2/l
v=37.1 m/s