Question

A weightless spring is stretched 10 cm by a suspended 1-kg block. If two such springs are used to suspend the block, one spring above the other, to effectively provide one double-length spring, then the total stretch of the double-length spring will be

Answer 1

Answer:

total stretch of the double-length spring will be 20 cm

Explanation:

given data

length x1 = 10 cm

mass = 1 kg

mass = double = 2 kg

to find out

the total stretch of the double-length spring will be

solution

we can say here spring constant is

k = mg    ............1

k is spring constant and m is mass and g is acceleration due to gravity

so for in 1st case and 2nd case with 1 kg mass and 2 kg mass

kx1 = mg   .........................2

and

kx2 = 2mg   ........................3

x is length

so from equation 2 and 3

$\frac{kx1}{kx2}= \frac{1mg}{2mg}$

$\frac{x1}{x2} = \frac{1}{2}$

$\frac{10}{x2} = \frac{1}{2}$

x2 = 20

so total stretch of the double-length spring will be 20 cm