Struggling to Solve a Spring + Gravity Problem

In summary, the conversation discusses a physics problem involving a mass attached to a spring and dropped from a vertical position. The maximum speed and distance the mass drops before coming to rest are calculated using both the potential energy of the spring and gravity, and just the potential energy of the spring. The speaker is struggling to solve the problem and is seeking help.
  • #1
underthebridge
12
0
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!
 
Physics news on Phys.org
  • #2
Anyone have any ideas? I'm really bothered by my inability to figure this problem out (><)
 
  • #3


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.
 

1. How do I set up the problem?

The first step in solving a spring + gravity problem is to identify the variables and forces involved. This includes the spring constant, mass of the object, gravitational acceleration, and any initial conditions. Then, use Newton's second law to set up the equation of motion.

2. What is the difference between a simple harmonic motion and a damped oscillation?

A simple harmonic motion is a type of oscillation where the restoring force is directly proportional to the displacement of the object. In a damped oscillation, there is an additional force (such as friction or air resistance) that causes the amplitude of the oscillation to decrease over time.

3. How do I solve for the period of oscillation?

The period of oscillation can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. This equation assumes that there is no damping or external forces acting on the system.

4. Can I use the same equation to solve for the amplitude of the oscillation?

No, the equation for the period of oscillation (T = 2π√(m/k)) cannot be used to solve for the amplitude. The amplitude is affected by initial conditions, such as the initial displacement and velocity of the object.

5. How do I incorporate gravity into the problem?

To incorporate gravity into the problem, you will need to include the gravitational acceleration (g) in your equation of motion. This will affect the equilibrium position of the object and may also affect the amplitude and period of oscillation.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
759
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
29
Views
823
  • Introductory Physics Homework Help
Replies
31
Views
972
  • Introductory Physics Homework Help
Replies
3
Views
408
  • Introductory Physics Homework Help
Replies
15
Views
133
  • Introductory Physics Homework Help
Replies
17
Views
238
  • Introductory Physics Homework Help
Replies
4
Views
743
  • Introductory Physics Homework Help
Replies
2
Views
716
  • Introductory Physics Homework Help
Replies
2
Views
887
Back
Top