Final answer:
To calculate the mass of the block, use the formula for velocity in simple harmonic motion. When the block is halfway between its equilibrium position and the endpoint, its displacement is half of the amplitude. Plugging in the given values, the mass of the block is approximately 82.72 kg.
Step-by-step explanation:
To calculate the mass of the block, we can use the formula for velocity in simple harmonic motion: v = √(k/m) * x, where v is the speed, k is the spring constant, m is the mass, and x is the displacement from the equilibrium position. In this case, when the block is halfway between its equilibrium position and the endpoint, its displacement is half of the amplitude, so x = 6.2 cm / 2 = 3.1 cm = 0.031 m. Plugging in the given values, we can solve for the mass:
- 35.8 cm/s = √(5 N/m) * m * 0.031 m
- 35.8 cm/s = √(0.155 N/m) * m
- 35.8^2 cm^2/s^2 = 0.155 N/m * m
- 1281.64 cm^2/s^2 = 0.155 N/m * m
- Simplifying the equation gives us: m = 1281.64 cm^2/s^2 / 0.155 N/m
- Converting cm^2/s^2 to m^2/s^2: m = 12.8164 m^2/s^2 / 0.155 N/m = 82.721 m/kg
- Rounding the answer to two decimal places gives: m = 82.72 kg