Springs...?

Question

If you have a spring which is 5 cms long and you add 100gs to the end and it stretches to 10 cms long, if you added ANOTHER 100gs how long would the spring be?

Answer 1

__________________________________________________________________________________
Force constant ' k '= Force' F' / extension ' x'

Extension 'x' of a spring=forceF / force constant k

When the spring is loaded with mass 'm', the force F=mg

mass m = 100 gram =0.1 kg

Force F=0.1 x g = 0.1 x 9.8 =0.98 newton

Extension=length after extension - unstretched length =(10 - 5) = 5 cm = 0.05 m

Force constant k=0.98 /0.05=98/5=19.6 N/m

When second load of 100 gram is added to first load ,the total load will be 200 gram =0.2 kg

Total stretching force later=0.2 x g = 0.2 x 9.8 =1.96 newton

total extension =total force / k=1.96 / 19.6=0.1 meter =10 cm

second extension= total extension - first extension

second extension=10 -5 =5 cm

Total length of the spring=original unstretched length + total extension

Total length of the spring after second extension= (5 +10)=15 cm

After second load of 100 g is suspended , total length of the spring will be=15 cm
_________________________________________________________________________________

Answer 2

The solution is
F=k*x
When 100g was added the spring elongated 10 cm
F=m*g=k*5
or
100*g=k*5
k=100*g/5

When another 100g gets added
200*g=(100*g/5)*x(note how I manipulated the units to stay in grams and cm)

x=10 cm, or the spring is now 15 cm long

j

Answer 3

The extension of a spring is proportional to the load provided the elastic limit is not exceeded.

15cms

Answer 4

15 cm unless it's elasticity was exceeded.