Question

A 39-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?

Answer 1

Answer:

The spring constant is 215.6 N/m.

Explanation:

Given that,

Distance = 39 cm

Compresses length = 29 cm

Mass = 2.2 kg

We need to calculate the distance

Using formula of distance

$x=l-l'$

Put the value into the formula

$x=39-29=10\ cm$

We need to calculate the spring constant

Using formula of restoring force

$F=kx$

$k=\dfrac{mg}{x}$

Where, F = force

x = distance

Put the value into the formula

$k=\dfrac{2.2\times9.8}{10\times10^{-2}}$

$k=215.6\ N/m$

Hence, The spring constant is 215.6 N/m.

Answer 2

The spring constant of the vertical spring having 39cm long  is 215.6N/m.

• Distance is given as: 39 cm, which is later compressed to 29 cmThen    

$Distance( x)= (39-29)=10cm$

Mass is given as 2.2 kg

• To calculate spring constant, we can use this formula;

$F= Kx$  ..........eqn(1) , $(F=mg)=( 9.8*2.2)= 21.56N$

make K subject of the formula

k=$\frac{ F }{ x }$

F= 21.56N and x=0.01m

$K= \frac{ 21.56 }{0.01 }$

$=215.6N/m$

Therefore, the answer is 215.6N/m.

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