# Finding Speed Using Conservation of Energy

• Mmm_Pasta
In summary, a massless spring with unstretched length of 0.45 m and spring constant of 122.3 N/m is attached to a block of mass 1.87 kg. The spring is stretched to a length of 1.1 m, and the block is released, shooting upward. Using conservation of energy, the speed of the block when it returns to the unstretched length of the spring is calculated to be approximately 3.9 m/s.
Mmm_Pasta

## Homework Statement

A massless spring has unstretched length Lo = 0.45 m and spring constant k = 122.3 N/m. A block of mass m = 1.87 kg is attached to the spring, and a student stretches the spring to a length of L = 1.1 m. Then the student releases the block and it shoots upward. What is the speed of the block when it returns to the position Lo for the first time?

Use gravity = 9.81 m/s2.

KE=1/2mv2
GPE=mgh
EPE=1/2kx2

## The Attempt at a Solution

Using conservation of energy, I set the energies at points. EPE when the spring is stretched is equal to KE and GPE at Lo. I got 1/2kx2=mgh + 1/2mv2. I found x by doing 1.1 m - 0.45 m. Since I am trying to find v I did 1/2kx2 - mgh = 1/2mv2. Then I plugged in the variables. 1/2(122.3 N/m)(0.65 m)2 - 1.87 kg(9.81 m/s2)(0.65 m) = 1/2(1.87 kg)v2. Doing the math I got 25.835875 J - 11.924055 J = (0.935 kg)v2. Which is 13.91182 J/0.935 kg = v2. My answer turned out to be 3.86 m/s, which turned out to be wrong.

3.85 should be correct...Do you know what your source says the answer is?

No, it does not have the answer listed. =(

Then who said it was wrong? Try using significant figure rule: v =3.9 m/s, maybe?

I entered 3.9. It's probably the program thingy I am using that is fault (second time if so). This problem is from an interactive example and is just for practice anyway.

## What is the conservation of energy?

The conservation of energy is a fundamental law in physics that states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

## How is conservation of energy used to find speed?

In order to find speed using conservation of energy, you need to know the initial and final energy of an object. By equating the initial energy (usually in the form of potential energy) to the final energy (in the form of kinetic energy), you can solve for the speed of the object.

## What are the units of speed?

The units of speed depend on the system of measurement being used. In the International System of Units (SI), speed is measured in meters per second (m/s). In the imperial system, it is measured in miles per hour (mph) or feet per second (ft/s).

## Can the conservation of energy be applied to all types of motion?

Yes, the conservation of energy can be applied to all types of motion as long as there are no external forces acting on the object. This means that the total energy of the system remains constant and can be used to calculate the speed of the object.

## What are some real-world applications of using conservation of energy to find speed?

The conservation of energy is used in many real-world applications, such as calculating the speed of a roller coaster or a car on a track, determining the speed of a projectile, and understanding the motion of pendulums and simple machines.

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