# How to solve for final velocity of object pushed by spring using concept of engergy

In summary, the given problem involves a glider attached to a spring on a track. The incorrect solution provided shows a misunderstanding of the system, as the spring pulls on the glider once it passes the unstretched position, resulting in a decrease in velocity. The correct answers for parts (a) and (b) are 1.47 m/s and 1.35 m/s respectively, which can be explained by the spring's pulling force.
Here is the given problem:

http://img213.imageshack.us/img213/6781/problemtk6.jpg

Here is my incorrect solution:

http://img152.imageshack.us/img152/6698/solutionzm3.jpg

Why should distance even matter for the final velocity in this problem since once the spring is uncompressed, the cart will continue at a steady velocity forever since there is no friction or air resistance?

The answer for (a) is 1.47 m/s, and the answer for (b) is 1.35 m/s. Again, why would the velocity be less for part (b) when there is no energy loss from either friction or air resistance?

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Because the problem says that the glider is attatched to the spring.

I think you have an incorrect mental picture of the system. The glider is attached to a spring which, in turn, is fixed to some point on the track (or attached to a wall, for instance). So, once the glider passes the unstretched position, the spring starts pulling instead of pushing, thus slowing the glider.

Ok, I was thinking the spring (which is attached to the glider) was compressed then allowed to push off of a wall and push the glider and spring backwards.

Last edited:

## 1. How do I calculate the final velocity of an object pushed by a spring?

In order to calculate the final velocity of an object pushed by a spring, you will need to use the formula: v = √(2m(kf-k0)). This formula takes into account the mass of the object (m), the spring constant (k), and the initial and final positions of the spring (kf and k0).

## 2. What is the concept of energy and how does it relate to solving for final velocity?

Energy is the ability to do work. In the context of solving for final velocity of an object pushed by a spring, we use the concept of energy because the energy stored in the spring is transferred to the object and causes it to move. This energy can be calculated using the formula: E = ½kx², where k is the spring constant and x is the displacement of the spring.

## 3. Is it necessary to know the spring constant in order to solve for final velocity?

Yes, the spring constant is a crucial factor in calculating the final velocity of an object pushed by a spring. The spring constant is a measure of the stiffness of the spring and is necessary in determining the amount of energy stored in the spring.

## 4. Can the final velocity of an object pushed by a spring be negative?

Yes, the final velocity of an object pushed by a spring can be negative. This indicates that the object is moving in the opposite direction of the initial displacement of the spring. This is often seen when the spring is compressed and the object is pushed in the opposite direction of the spring's initial position.

## 5. Are there any other factors that may affect the final velocity of an object pushed by a spring?

Yes, there can be other factors that may affect the final velocity of an object pushed by a spring. Some examples include friction, air resistance, and the elasticity of the spring material. These factors may cause the actual final velocity to differ from the calculated value.

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