Question

7.20 a 1.20-kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 n/m that is com- pressed 15.0 cm. when the spring is released, how high does the cheese rise from this initial position? (the cheese and the spring are not attached.)

Answer 1

The cheese will rise approximately 0.087 meters (or 8.7 centimeters) from its initial position.

explanation

The direct answer for each part:

- Force constant, k = 1800 N/m

- Compression of the spring, x = 15.0 cm = 0.15 m

- Weight of the cheese, W = mg = 1.20 kg * 9.81 m/s² ≈ 11.772 N

- Potential energy stored in the spring at maximum compression, PE = 0.5 * k * x²

- PE = 0.5 * 1800 N/m * (0.15 m)² ≈ 20.25 J

- Maximum potential energy = Weight of the cheese * Maximum height reached

- Maximum height = PE / W ≈ 20.25 J / 11.772 N ≈ 1.722 m

- The cheese will rise approximately 0.087 meters (or 8.7 centimeters).

The potential energy stored in the compressed spring equals the potential energy gained by the cheese when released. With the given force constant and compression of the spring, calculating the stored potential energy allows determining the maximum height the cheese can reach.

Utilizing the formula for potential energy stored in a spring (PE = 0.5 * k * x²), where 'k' represents the spring constant and 'x' is the compression distance, and equating this energy to the potential energy at maximum height (PE = mgh), we find the height the cheese reaches upon release. Consequently, the cheese rises approximately 0.087 meters (8.7 centimeters) from its initial position. This calculation assumes no energy losses due to air resistance or other dissipative factors in the system.