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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 :

cjmejiab

To solve this problem we will apply Hooke's law. Which says that the force on a spring is equivalent to the product between the elastic constant and the displacement of the spring.

[tex]F = k x[/tex]

Here,

k = Spring constant

x = Displacement

Rearranging to find the spring constant,

[tex]k = \frac{F}{x}[/tex]

Spring compresses it to 29 cm so

[tex]x = 39- 29 = 10 cm[/tex]

[tex]k = \frac{mg}{x} \rightarrow[/tex] The force in this case is equivalent to the weight of the spring

[tex]k = \frac{2.2 * 9.8}{10 * 10 ^ {-2}}[/tex]

[tex]k = 215.6N/m[/tex]

Therefore the spring constant is 215.6N/m

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