Hi,

I'm trying to solve a problem with two different methods, but I can't seem to get to the same answer with both methods, I don't understand where I'm making a mistake.

Here is the problem: A mass of 1 kg is resting on top of a spring in the vertical position. The spring's constant is of 20 N/m. Find the lenght of the spring's compresses.

Method 1

F spring = F gravity

KX = mg

20 * X = 1 * 9.8

X = 9.8 / 20 = 0.49 m

Spring compresses 49 cm down.

Method 2

Elastic energy = Initial potential gravity engergy

.5KX² = mgX (since the height lost by the mass is the compression, X)

.5 * 20 * X² = 1 * 9.8 * X

10 X² - 9.8X = 0

X (10X - 9.8) = 0

X = 0 or 10X -9.8 = 0

Dismiss X=0 since it is the initial state

Hence X = .98

Spring compresses 98 cm Down.

The difference between method 1 and 2 is a factor of 2. I have also come across other situations when solving the problem with forces or energy i get the same factor of 2 difference. Can someone help me understand my mistake?

Thanks!

I'm trying to solve a problem with two different methods, but I can't seem to get to the same answer with both methods, I don't understand where I'm making a mistake.

Here is the problem: A mass of 1 kg is resting on top of a spring in the vertical position. The spring's constant is of 20 N/m. Find the lenght of the spring's compresses.

Method 1

F spring = F gravity

KX = mg

20 * X = 1 * 9.8

X = 9.8 / 20 = 0.49 m

Spring compresses 49 cm down.

Method 2

Elastic energy = Initial potential gravity engergy

.5KX² = mgX (since the height lost by the mass is the compression, X)

.5 * 20 * X² = 1 * 9.8 * X

10 X² - 9.8X = 0

X (10X - 9.8) = 0

X = 0 or 10X -9.8 = 0

Dismiss X=0 since it is the initial state

Hence X = .98

Spring compresses 98 cm Down.

The difference between method 1 and 2 is a factor of 2. I have also come across other situations when solving the problem with forces or energy i get the same factor of 2 difference. Can someone help me understand my mistake?

Thanks!

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