Struggling to Solve a Spring + Gravity Problem

[underthebridge]

I can't seem to wrap my brain around this problem. My prof did an example in class that I completely understood, but when I apply the same technique here my answer is not coming out correctly.

A 10-g mass is attached to the end of an unstressed, light, vertical spring (k = 49 N/m) and then dropped. Answer the following questions by considering the potential energy due to the spring plus the potential energy due to gravity, i.e. measure distances from the equilibrium position of the spring with no mass attached. (a) What is the maximum speed of the falling mass? (b) How far does the mass drop before coming to rest momentarily? (c) Repeat (a) and (b), but answer the questions by considering the potential energy of the spring with the mass attached, i.e. measure distances from the equilibrium position of the spring with the mass attached.

As it turns out, the maximum velocity is 14 cm/s and the distance it drops before coming to a momentary rest is 4 mm.

In solving for the distance, I went the route he took in class which is as follows:

Net Force = 0
-Fspring - Fgravity = 0
-kx - mg = 0

Assuming g = 9.8, when I plug in the rest of the values I get a -.002 m for x, the negative of course falling in line with assuming that the initial position is 0 and it moves downward. This of course does not agree with the 4 mm answer I should be coming to.

As far as maximum velocity is concerned, well there is an initial potential due to gravity as well as an initial potential due to the spring (which can be eliminated by setting the initial position at 0, right?) and a final potential due to the spring as well as a final kinetic energy.

All of this is according to part c as far as I can tell, as the mass of the block is considered in the problem. I think I kind of understand it, though by no means do I have a grasp on it (as you can see). But this also leaves out solving any of it without considering the mass to be a part of the problem, as is asked in parts a and b.

Any and all help would be much appreciated!

 

[underthebridge]

Anyone have any ideas? I'm really bothered by my inability to figure this problem out (><)

 

[wais]

It sounds like you are on the right track with your approach to solving this problem. It can definitely be challenging to wrap your head around problems involving both spring and gravity forces. One suggestion I have is to double check your calculations and make sure you are using the correct units. In this case, the mass is given in grams but the spring constant is given in N/m, so you may need to convert the mass to kilograms before plugging it into your equation.

Additionally, for part (a), you can use the conservation of energy principle to solve for the maximum velocity. This means that the initial potential energy (due to the spring and gravity) will be equal to the final kinetic energy. So you can set up an equation like this:

(1/2)kx^2 + mgh = (1/2)mv^2

Where x is the distance the mass has stretched the spring, h is the height the mass has dropped, and v is the maximum velocity. You can solve for v using this equation.

For part (b), you can use a similar approach but set the final kinetic energy to 0 since the mass comes to a momentary rest. This will give you the distance the mass has dropped before coming to rest.

I hope this helps and good luck with your problem solving! Remember to always double check your calculations and units to make sure you are on the right track. And don't be afraid to ask your professor or classmates for help if you are still struggling.