Calculating Spring Constant and Energy Conservation: How Fast Will the Bag Drop?

In summary: So GPE lost = (3)(9.8)(d) where d is the distance the bag drops before starting to come back. And then GPE gained = 1/2kx^2 where x is the displacement when the bag comes back to its starting point. So we can set these equal to each other and solve for x. Once we have x, we can find the velocity at that point using KE=1/2mv^2. And for the acceleration, it will be 0 at the highest and lowest points since the velocity is changing direction. At the middle point, the acceleration will be equal to the spring force, which can be calculated using F=kx. In summary, we can calculate the spring constant
  • #1
MarieMarie94
2
1
1. Problem Statement:
A vertical spring has one end attached to the ceiling and a 3kg bag attached to the other one. When the system is at rest, the spring is stretched by 40cm. 1) determine the spring constant. 2) Let the bag drop from a position in which the spring is not deformed. Using the conservation of energy law, find: how fast the bag is moving after it drops 40 cm, and how far down the bag will drop before starting to come back. Calculate and show the direction of the bag's acceleration when the bag is at the highest, lowest, and middle of the oscillation positions.

Homework Equations

:[/B]
K=mg/x
KE=1/2m(v^2)
GPE=mgh
EPE=1/2k(x^2)

3. Attempt at the Solution:
So I found a spring constant. I'm not sure if it's correct but I got, k=(3)(9.8)/(.4)= 73.5 N/m. I ran into problems with the rest though. For finding the velocity of the bag dropping 40cm, I did GPE=KE+EPE but I'm not sure if that's right. As for the farthest distance the bag would drop and the acceleration, I wasn't exactly sure how to approach them.

Update: To find the velocity at 40cm, should it actually only be GPE=KE because we're treating the 40cm as our equilibrium? And then to find the farthest distance the bag would drop would it be GPE=EPE to find our displacement? Or am I completely wrong?
 
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  • #2
MarieMarie94 said:
GPE=KE+EPE
GPE lost = KE gained + EPE gained, yes.
MarieMarie94 said:
to find the farthest distance the bag would drop would it be GPE=EPE to find our displacement
Yes, but what is the GPE lost in this case?
 
  • #3
haruspex said:
Yes, but what is the GPE lost in this case?
Would it be (3)(9.8)(d) because we don't know the distance?
 
  • #4
MarieMarie94 said:
Would it be (3)(9.8)(d) because we don't know the distance?
Right.
 

1. What is spring conservation of energy?

Spring conservation of energy is a physical law that states that the total amount of energy in a closed system remains constant over time. In the context of a spring, this means that the total energy of the spring (potential energy + kinetic energy) remains the same as long as there are no external forces acting on it.

2. How does the spring conservation of energy apply to everyday objects?

Spring conservation of energy applies to everyday objects in the sense that it explains the behavior of objects that are attached to springs, such as a bouncing ball or a door closer. The spring in these objects stores potential energy when it is compressed or stretched, and this energy is converted to kinetic energy when the spring is released.

3. What factors affect the amount of energy stored in a spring?

The amount of energy stored in a spring depends on two factors: the spring constant and the distance the spring is compressed or stretched. The spring constant is a measure of the stiffness of the spring, and a higher value means the spring will store more energy for a given displacement.

4. Can energy be lost in a spring system?

In an ideal system with no external forces, energy cannot be lost in a spring system. However, in real-world situations, some energy may be lost due to factors such as friction and air resistance. This means that the total energy of the system may decrease over time, but the principle of conservation of energy still holds true.

5. How is the law of conservation of energy related to the spring constant?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total energy in a spring system, including the potential and kinetic energy of the spring, remains constant. The spring constant is a measure of the potential energy stored in the spring, and as long as the spring remains in the same system, this energy cannot be lost or created.

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