Why can gravitational potential energy be ignored in a verticle spring with a hanging mass? My...

Why can gravitational potential energy be ignored in a verticle spring with a hanging mass? My TA mentioned something about no work being done by GPE, but that doesn't really make sense. Also, the assignment is asking for it to be explained conceptually, not with equations. Thanks!

Expert Solution

Thee (massless) spring hangs vertically with a block of mass m attached at the bottom. We could calculate how much the spring is stretched by equating the gravitational and spring forces (kx1=mgkx1=mg).

Now, during the pulling process ,positive work is being done on the system, which means that the energy in the system increases.

Let's use the work-energy theorem,

Wnet,external (Positive) =?Etot =?Ugrav (Negative) + ?Uelastic (Positive)

The gravitational potential energy decreases. Where does it go? Well, the only other term that could (mathematically) compensate for this decrease in gravitational potential energy is the increase in elastic potential energy. The spring is not storing gravitational potential energy; rather, gravitational potential energy was converted to elastic potential energy.

The left-hand side of the equation above is positive, the absolute value of ?Uelastic is greater than that of ?Ugrav. So, not only was the gravitational potential energy converted to elastic potential energy, the positive work done on the system also adds to the increase in elastic potential energy.

genius_generous answered 1 year ago

How can the gravitational potential energy of something be negative?

A mass hanging from a spring oscillates with a period of 0.35 s. Suppose the mass...

A mass hanging from a spring oscillates with a period of 0.35 s. Suppose the mass and spring are swung in a horizontal circle, with the free end of the spring at the pivot. What rotation frequency, in rpm, will cause the spring’s length to stretch by 15%?

A 8.50 kg mass is attached to the end of a hanging spring and stretches it...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it 28.0 cm. It is then pulled down an additional 12.0 cm and then let go. What is the maximum acceleration of the mass? At what position does this occur? What is the position and velocity of the mass 0.63 s after release?

1. Assume that hanging a 100 gram mass from a given spring stretches the spring by...

1. Assume that hanging a 100 gram mass from a given spring stretches the spring by 2 cm. If two springs of this kind are connected back to back (series configuration), how much would the combination stretch if a 200 gram mass is suspended? a. 1 cm b. 2 cm c. 3 cm d. 4 cm e. none of these 2. What would be the answer to the previous question if the two springs were connected in parallel configuration? a....

An ideal spring is in equilibrium, hanging from a ceiling with a 1 kg mass at...

An ideal spring is in equilibrium, hanging from a ceiling with a 1 kg mass at the end. At rest, the length of the hanging spring is 10 cm. Then, an additional 5 kg block is added to the spring, causing its length at rest to increase to 13 cm. The 5 kg block is then removed. Starting from rest, when the 5 kg block is removed, the spring begins to oscillate. What will the spring’s velocity be, the third...

You have a spring hanging vertically. You add a mass to the end and let it...

You have a spring hanging vertically. You add a mass to the end and let it stretch to find its new equilibrium position which is 3.17 cm below the unstretched position. You now raise the mass (compress the mass-spring system) to its original unstretched position. Now you release the mass. How far from this starting position does it travel downward until it stops and changes direction?

A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes...

A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes to rest at its equilibrium position. The spring constant is 4 lb/ft and there is no damping. A. How far (in feet) does the mass stretch the spring from its natural length? L= B. What is the resonance frequency for the system? ω0= C. At time t=0 seconds, an external force F(t)=3cos(ω0t) is applied to the system (where ω0 is the resonance frequency from...

An 7-kg mass is attached to a spring hanging from the ceiling and allowed to come...

An 7-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 50 N/m and the damping constant is 4 N-sec/m At time t=0, an external force of 8sin(3t)cos(3t) is applied to the system. Determine the amplitude and frequency of the steady-state solution.

The potential energy stored in the compressed spring of a dart gun, with a spring constant...

The potential energy stored in the compressed spring of a dart gun, with a spring constant of 36.00 N/m, is 1.440 J. Find by how much is the spring is compressed. A 0.070 kg dart is fired straight up. Find the vertical distance the dart travels from its position when the spring is compressed to its highest position. The same dart is now fired horizontally from a height of 4.30 m. The dart remains in contact until the spring reaches...

determine the potential energy stored in a spring if a force of 28 holds the spring...

determine the potential energy stored in a spring if a force of 28 holds the spring and it has a spring constant of 97 N/m compressed. please answer in joules and explain how you solved It. (like dumb it down) so that I could learn. thank you!

Question