Use the following figure to answer the question:
-A spring is stretched 10 cm by a suspended 1-kg block.If two such springs side-by-side are used to suspend the block,so each spring supports half the weight of the block,then each spring will stretch
A)5 cm.
B)10 cm.
C)20 cm.
D)30 cm.
E)none of these

Question

Use the following figure to answer the question: 
-A spring is stretched 10 cm by a suspended 1-kg block.If two such springs side-by-side are used to suspend the block,so each spring supports half the weight of the block,then each spring will stretch
A)5 cm. 
B)10 cm. 
C)20 cm. 
D)30 cm. 
E)none of these

Quizplus · Accepted Answer

When one spring supports the 1-kg block, it stretches 10 cm. This means that the spring constant, k, is:

F = kx

where F is the force applied by the spring (in newtons), and x is the displacement of the spring from its equilibrium position (in meters).

For a 1-kg block hanging from the spring, the weight of the block is:

Fg = mg = (1 kg)(9.8 m/s^2) = 9.8 N

Since the spring is stretched 10 cm (or 0.1 m), we can solve for k:

9.8 N = k(0.1 m)
k = 98 N/m

Now, if we use two springs side-by-side, each spring must support half the weight of the block (or 4.9 N). The displacement of each spring can be found by solving:

4.9 N = kx

where k is still 98 N/m (since the springs are the same), and x is the displacement we're solving for. Rearranging this equation, we get:

x = 4.9 N / 98 N/m
x = 0.05 m

Converting this back to centimeters, we get:

x = 5 cm

Therefore, each spring will stretch 5 cm when supporting half the weight of the block.

Use the Following Figure to Answer the Question