Work and Potential/Kinetic Energy (spring problem)

In summary, the problem involves a ball with a mass of .360kg being dropped from a height of 1.20 meters onto a fixed vertical spring with a force constant of 350 N/m. The goal is to find the speed of the ball when the spring has been compressed 5.0cm and the maximum distance the spring is compressed by the ball. The equations used are Work=F*D, Potential Energy (PE)=1/2*K(xf-xi)^2, Change in Potential Energy (ΔU)=mg*Δy, and Conservation of Energy (Ki+Ui=Kf+Uf). The solution involves finding the changes in potential energy and using the remaining potential energy to determine kinetic energy.
  • #1
stevebrstlct
4
0

Homework Statement


A)
A ball with a mass of .360kg is dropped from a height of 1.20 meters above the top of a fixed vertical spring, whose force constant is 350 N/m. What is the speed of the ball when the spring has been compressed 5.0cm?
(Ignore the mass of the spring; also, notice that this problem contains both forms of potential energy (gravitational and spring pot'l En.)

B)
What is the maximum distance the spring is compressed by the ball?

Homework Equations


Work=F[tex]\cdot[/tex]D
PE:
U=1/2K(xf-xi)2
[tex]\Delta[/tex]U=mg[tex]\cdot[/tex][tex]\Delta[/tex]Y
Ki+Ui=Kf+Uf

m=.360 Kg
H=1.2m
[tex]\Delta[/tex]X=5.0 cm
K=350 Nm


The Attempt at a Solution


We did a problem similar to this on a frictionless horizontal plane. We used the conservation of energy to solve it. In the picture we drew we found where the Pot. and Kin. energies were zero which left the equation with only one unknown left. In that problem there was constant velocity but in the problem I just posted we have an acceleration of mg down which leaves me confused on what the right way to solve this is. I also know for part B the velocity will be 0.
 
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  • #2
Welcome to PF.

Figure your changes in potential energy.

m*g*h = .36*9.8*(1.2 + .5)

Now how much potential energy is in the spring?

1/2*k*x2

Whatever is left over then must be kinetic energy right?
 
  • #3
Wow that makes much more sense now, thanks alot!
 

1. What is the definition of work in relation to potential and kinetic energy?

The scientific definition of work is the product of the force applied to an object and the distance over which the force acts. In the context of potential and kinetic energy, work is the energy transferred to or from an object by a force, resulting in a change in the object's potential or kinetic energy.

2. How is potential energy related to a spring?

Potential energy is the stored energy that an object possesses due to its position or configuration. In the context of a spring, potential energy is stored in the spring when it is compressed or stretched from its equilibrium position. This potential energy is then converted into kinetic energy when the spring is released and returns to its equilibrium position.

3. What is the formula for calculating the potential energy of a spring?

The formula for calculating the potential energy of a spring is P.E. = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position. This formula assumes that the spring is being stretched or compressed in a linear fashion.

4. How is kinetic energy related to a spring?

Kinetic energy is the energy an object possesses due to its motion. In the context of a spring, kinetic energy is the energy that the spring possesses when it is in motion as a result of being released from a compressed or stretched state. It is equal to the potential energy that was stored in the spring before it was released.

5. How can the conservation of energy be applied to a spring problem?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted. In a spring problem, this means that the total amount of energy (potential energy + kinetic energy) in the system remains constant, even as the energy is transferred between the spring and the object it is acting upon. This concept can be used to solve for unknown variables in a spring problem, such as the displacement or velocity of the object.

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