Problem 3. A 10 cm long spring is attached to the ceiling....

Problem 3. A 10 cm long spring is attached to the ceiling. When a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm. (a) What is the spring constant $k$? (5 points) (b) How long is the spring when a 3.7 kg mass is suspended from it? (5 points)

Transcript

00:02 Okay, so now we have a problem where we have a spring attached to a ceiling and we're going to hang a mass from it and when that mass is equal to two kilograms we get a stretch length of 15 centimeters again every time they give a centimeters.

00:21 Let's just convert it to meters.

00:22 0 .15 meters and the question is what is the spring constant? so this is a newton's second lie equation sigma f is equal to m a i'm going to draw a free body diagram that for this mass i've got a force of spring pulling upward that should be an s force of spring pulling upward and i've got a force of gravity pulling downward and so my forces are my let's go ahead and just say up is positive so f s minus fg is equal to my mass times acceleration but if i'm just hanging it from there, that acceleration is equal to zero.

01:08 And so i've got fs is equal to fg.

01:11 And my fs is just k times x.

01:15 My fg is just m times g.

01:19 And so again, i said this in an earlier video.

01:24 Be very, very careful with this equation.

01:26 Sometimes there's a minus sign associated with it.

01:28 All that minus sign tells you is which direction to draw the arrow.

01:32 We know the spring's pulling up, we've got no business having that minus sign in the mix.

01:37 And so i'm solving for k.

01:39 K is going to equal to mg divided by x.

01:42 I know my mass is 2.

01:44 I know my g is 9 .8.

01:47 I know my g is 0 .15.

01:50 And we're going to plug that into our calculator.

01:55 9 .8 times 2 divided by 0 .15.

01:59 That's 130 point a whole bunch of sixes...

Question

Problem 3. A 10 cm long spring is attached to the ceiling. When a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm. (a) What is the spring constant $k$? (5 points) (b) How long is the spring when a 3.7 kg mass is suspended from it? (5 points)

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