# Homework help: Work and Energy: Spring

• Syeda
In summary, a loaded toy with a spring constant of 8000 N/m and a mass of 0.5 kg is compressed by 0.05 m and then fired on a flat surface. The toy is released with a speed of 28.284 m/s and if it approaches a hill, it can climb a maximum height of 2.04 m.
Syeda

## Homework Statement

A .5 kg loaded toy (spring k=8000 n/m) loaded toy is compressed .05 m and fired on a flat surface
a) Find the new speed it was released with
b) If it approaches a hill find the maximum height it can climb

KE=1/2kx²
KE=1/2mv²
PE=1/2kx^2

## The Attempt at a Solution

a) KE= 1/2(8000N/m)(.05m)²
KE=200J

KE=1/2mv²
200J=1/2(.5kg) v²
v= 28.284 m/s

b) PE=1/2kx^2
PE=10J
PE=mgh
10=.5kg(9.8m/s²)x
2.04m=h

Last edited:
In part (a), check your calculation of spring potential energy. Interestingly, you used the correct value for energy in part (b).

Syeda
gneill said:
In part (a), check your calculation of spring potential energy. Interestingly, you used the correct value for energy in part (b).
Thank you for catching my mistake! I forgot to square the values so this is what I got for part a now:
10=1/2(.5)v²
v=6.32m/s

That looks better. I think you're all good now.

Syeda

## 1. What is a spring and how does it work?

A spring is an elastic object that can be stretched or compressed and will return to its original shape when the force is removed. It works by storing potential energy when it is stretched or compressed, and releasing that energy when it returns to its original shape.

## 2. How is the potential energy of a spring calculated?

The potential energy of a spring is calculated using the formula PE = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position. The higher the spring constant, the stiffer the spring and the more potential energy it can store.

## 3. Can a spring have negative potential energy?

Yes, a spring can have negative potential energy. This occurs when the spring is compressed and the displacement (x) is negative. This indicates that the spring is in a lower energy state and has the potential to release energy when it returns to its equilibrium position.

## 4. What is the relationship between the force exerted by a spring and its displacement?

According to Hooke's Law, the force exerted by a spring is directly proportional to its displacement from the equilibrium position. This means that the more a spring is stretched or compressed, the greater the force it exerts.

## 5. How is the work done by a spring calculated?

The work done by a spring is calculated using the formula W = 1/2kx^2, where k is the spring constant and x is the displacement from the initial to final position. This formula represents the change in potential energy of the spring, which is equal to the work done on the spring.

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