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The problem states:

>A 2-gram coin is pushed down, pressing it against a vertical spring by compressing the spring by 1 cm. The spring constant is 40 N/m. To what height from its original position will the coin jump when the spring is released?

Let's solve this step-by-step.

### Solution:
1. **Identify given values:**
   - Mass of the coin, \( m = 2 \, \text{g} = 0.002 \, \text{kg} \)
   - Compression of the spring, \( x = 1 \, \text{cm} = 0.01 \, \text{m} \)
   - Spring constant, \( k = 40 \, \text{N/m} \)

2. **Energy stored in the compressed spring:**
   The elastic potential energy \( U \) in a compressed spring is given by:
   \[
   U = \frac{1}{2} k x^2
   \]
   Substituting the values:
   \[
   U = \frac{1}{2} \cdot 40 \cdot (0.01)^2 = \frac{1}{2} \cdot 40 \cdot 0.0001 = 0.002 \, \text{J}
   \]

3. **Convert spring energy to gravitational potential energy:**
   When the spring releases, this energy is converted into gravitational potential energy \( U_g \) at the maximum height \( h \), given by:
   \[
   U_g = m g h
   \]
   Setting \( U = U_g \):
   \[
   0.002 = 0.002 \cdot 9.8 \cdot h
   \]
   Solving for \( h \):
   \[
   h = \frac{0.002}{0.002 \cdot 9.8} = \frac{0.002}{0.0196} \approx 0.102 \, \text{m} = 10.2 \, \text{cm}
   \]

### Answer:
The coin will jump to a height of approximately **10 cm**.

Would you like further details or have any questions?

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### Additional Practice Questions:
1. If the spring constant were doubled, how high would the coin jump?
2. How would the jump height change if the mass of the coin was 4 grams instead of 2 grams?
3. If the coin were pressed down by 2 cm instead of 1 cm, what would be the new height it reaches?
4. Calculate the spring's potential energy if compressed by 5 cm.
5. What would happen to the height if the experiment were conducted on the Moon, where gravity is 1.62 m/s²?

#### Tip:
Remember, the energy in a spring depends on the square of the compression distance. Doubling the compression will quadruple the stored energy!

Una moneda de 2 gramos de masa se empuja hacia abajo apretándola contra un resorte vertical, comprimiendo a dicho resorte en 1 cm. La constante elástica del resorte es de 40 N/m. Hasta qué distancia de su posición original saltará la moneda cuando suelte el resorte?

Solve an energy conservation problem where a 2-gram coin is pressed against a vertical spring, compressing it by 1 cm. Given the spring constant of 40 N/m, learn how to calculate the height the coin will reach upon release using elastic and gravitational potential energy. Suitable for high school students.

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