How Much Work is Done by a Spring on a Sliding Ladle?

In summary, the ladle attached to a spring with a spring constant of 490 N/m has a kinetic energy of 10 J as it passes through its equilibrium position. When the spring is compressed by 0.10 m and the ladle is moving away from the equilibrium position, the spring does work at a rate of 4.9 J.
  • #1
bikerboi92
8
0
Ladle Attached to Spring A 0.23 kg ladle sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (with k = 490 N/m) whose other end is fixed. The mass has a kinetic energy of 10 J as it passes through its equilibrium position (the point at which the spring force is zero).

(a) At what rate is the spring doing work on the ladle as the ladle passes through its equilibrium position?

i got this correct: 0 watts

(b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position?
 
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  • #2
bikerboi92 said:
(b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position?

First you must find the force in the spring at x=.1m which can be found through the equation F=kx. Therefore, the force will be 49N. Then you know that WORK=FORCE*DISTANCE. Therefore W=(49N)*(.1m)=4.9J. This should be correct, though it might be negative.
 
  • #3
[/B]

The rate at which the spring is doing work on the ladle can be calculated using the formula for work done by a spring, which is W = 1/2*k*x^2, where k is the spring constant and x is the distance the spring is compressed or stretched. In this case, the ladle is moving away from the equilibrium position, so the spring is being stretched.

We can use the given information to calculate the distance the spring is being compressed. Since the ladle has a kinetic energy of 10 J when passing through the equilibrium position, we can use the formula for kinetic energy, KE = 1/2*m*v^2, where m is the mass of the ladle and v is its velocity, to find the velocity of the ladle at the equilibrium position.

10 J = 1/2 * 0.23 kg * v^2

v = √(10 J * 2 / 0.23 kg) = 6.47 m/s

Now, using the conservation of energy principle, we can find the maximum compression distance of the spring by equating the kinetic energy of the ladle at the equilibrium position to the potential energy stored in the spring when compressed.

1/2 * 0.23 kg * (6.47 m/s)^2 = 1/2 * 490 N/m * x^2

x = √(0.23 kg * (6.47 m/s)^2 / 490 N/m) = 0.10 m

Therefore, when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position, the spring is doing work on the ladle at a rate of:

W = 1/2 * 490 N/m * (0.10 m)^2 = 2.45 J/s = 2.45 watts

Therefore, the spring is doing work on the ladle at a rate of 2.45 watts when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position.
 

1. What is a spring?

A spring is an elastic object that can be stretched or compressed by an external force. It has the ability to store potential energy when stretched or compressed and release it when the force is removed.

2. How does a spring store energy?

A spring stores energy by deforming or changing its shape when a force is applied to it. This deformation creates potential energy in the spring, which is then released when the force is removed.

3. What is the relationship between the force applied to a spring and its displacement?

The relationship between the force applied to a spring and its displacement is described by Hooke's Law, which states that the force applied is directly proportional to the displacement of the spring. This means that as the force increases, the displacement of the spring also increases.

4. How is the energy of a spring calculated?

The energy of a spring can be calculated using the formula E = 1/2kx^2, where E is the energy in joules, k is the spring constant in newtons per meter (N/m), and x is the displacement of the spring from its equilibrium position in meters.

5. How are springs used in everyday life?

Springs are used in various everyday objects, such as mattresses, trampolines, and car suspensions. They are also used in tools and instruments, like pogo sticks and weighing scales, to provide a spring force and store energy. In addition, springs are used in clocks and watches to regulate timekeeping.

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