How Is the Spring Constant Calculated from Oscillation and Mass Changes?

[ConstableZiM]

Homework Statement

A 100g object is suspended from a spring. When 40g are added, the spring stretches an additional 5.0cm. With the total mass of 140g, the spring is set into vertical oscillations with an amplitude of 10 cm. (a) What is the force constant of the spring?

Homework Equations

$$\sum$$ F = 0 = -kx + mg

The Attempt at a Solution

From what I know, the force required to stretch a spring is not linear, so I am guessing that plugging just the 40 grams and the 5 cm into the equation won't work... What I got when I did that was k = 0.040kg * 9.8 / 0.05m = 7.84

Im guessing this is wrong?

Help would be appreciated.

 

[SEngstrom]

The usual assumption about springs is that the force exerted by them is indeed linear (as in #2 above). All your solution needs is units. (Not all information given in the problem is necessary to solve it.)

 

[collinsmark]

From what I know, the force required to stretch a spring is not linear, so I am guessing that plugging just the 40 grams and the 5 cm into the equation won't work...

Even for a real-world spring, as long as you don't stretch the spring so much that it plastically deforms or collapses onto itself, the relationship between force and stretching distance can be approximated quite well using Hooke's law, F = kx (some authors define it as F = -kx). Here F is directly proportional to x, so it is linear.

What I got when I did that was k = 0.040kg * 9.8 / 0.05m = 7.84

'Looks okay to me.

[Edit: SEngstrom beat me to the answer. And as SEngstrom says, don't forget your units. ]

 

[ConstableZiM]

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