The bottom of a spring hanging from the ceiling lies 1.6 m below the ceiling. A

Question

The bottom of a spring hanging from the ceiling lies 1.6 m below the ceiling. A block of mass 3.0 kg Is attached to the bottom of the spring and lowered slowly enough not to start the system osculating, finally when the Nock stops dropping and Is released, the bottom of the spring is now 1.9 m below the ceiling, what it the weight of the block? That is, what is the magnitude of the force with which the earth attracts the block? (For this part, one can Ignore the spring.) Now consider the spring. What force docs it exert on the mass? Use a positive (negative) number If up (down). Remember that the block Is not moving. Tries 0/10 What is the spring constant k?

Explanation / Answer

Note:-
In gravitational related problems you have to use g. The value g=9.81 m/s^2 is more close value. But sometimes g=10 m/s^2 is used for calculation ease.
I am using g=9.81 m/s^2 here. Your answers may be according to g=10.

1) First Part...
The weight of the block
W = mass*gravitational acceleration = 3kg*9.81m/sec-square
= 29.43 N
--Magnitude of the force with which the earth attracts the block
= Weight of the block
Force = 29.43 N

2) Second part...
The block is finally in stable state
So force exerted on block by spring = weight of the block
Fs = 29.43 N

3) Third part...
The expansion in the spring is equal to 1.9 m - 1.6 m = 0.3 m = x
Tension force in spring = spring constant*expansion = weight of the block
(.... spring force balances the gravitational force on the block...)
Let the expansion is 'x' and spring constant is K
Then Kx = block weight = 29.43
K(0.3) = 29.43
K = 29.43/0.3
K = 98.1 N/m
So this K=98.1 N/m is the spring constant K.

###Note: If you pick the value of g=10 m/sec^2 then the weight of the block will be equal to 30 N and the spring constant will be 100 N/m. And spring will exert the force on the block equal to 30 N.

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