# Mass launched into the air by a spring

• jybe
In summary, the conversation discusses a child's toy that is attached to a spring and is released from a compressed position. The toy has a mass of 117 g and rises to a height of 45.0 cm, allowing for an estimation of the force constant of the spring. The solution involves using the equation 0.5kx^2 = mgh and converting centimeters to meters, resulting in a force constant of 258248.25 N/m. However, the answer is off by a factor of 10, possibly due to the storage of potential energy in the spring.
jybe

## Homework Statement

A child's toy consists of a piece of plastic attached to a spring in the figure below. The spring is compressed against the floor a distance of 2.00 cm, and the toy is released. If the toy has a mass of 117 g and rises to a maximum height of 45.0 cm, estimate the force constant of the spring. (Assume the toy rises 45.0 cm above the equilibrium position of the spring.)

0.5kx^2 = mgh

## The Attempt at a Solution

k = 2mgh/(x^2)

k = 2*0.117*9.81*45/(0.02^2)

k = 258248.25 N/m

Apparently this answer is off by a multiple of 10... not sure what's wrong. Can anybody help me? Thanks

You forgot to convert 45 cm to meters. Also, some of the stored potential energy in the spring is used to raise the toy from where it starts to the equilibrium position. I am not sure if that will account for a factor of 10 though. More like a factor of 100.

## 1. What is the relationship between the mass launched and the spring?

The mass launched into the air by a spring is directly related to the properties of the spring, such as its stiffness and compression. The greater the stiffness of the spring and the more it is compressed, the greater the mass that can be launched into the air.

## 2. How does the launch angle affect the distance the mass travels?

The launch angle, or the angle at which the mass is launched into the air, plays a significant role in determining the distance the mass travels. The optimal launch angle for maximum distance is typically between 45-60 degrees, depending on the specific properties of the spring and the mass.

## 3. What factors influence the height the mass reaches?

The height the mass reaches is influenced by several factors, including the initial compression of the spring, the launch angle, and the mass of the object. Additionally, air resistance and other external forces may also play a role in determining the maximum height the mass can reach.

## 4. Can the mass launched into the air be calculated using a formula?

Yes, there are several formulas that can be used to calculate the distance and height the mass will reach when launched by a spring. These formulas take into account the properties of the spring, the initial compression, and the launch angle to determine the trajectory of the mass.

## 5. How does the mass of the object affect the launch distance?

The mass of the object being launched does have an impact on the launch distance, as a heavier object will require a stronger spring and more initial compression to achieve the same distance as a lighter object. However, the launch angle and other factors also play a significant role in determining the overall launch distance.

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