detrmine the maximum vertical displacment d of apan of negligable mass is attached to two identical springs of stiffness k=250n/m and a10 kg box is dropped from aheight of 0.5m above the pan
To determine the maximum vertical displacement of the pan, we need to consider the potential energy gained by the box as it falls and gets converted into potential energy stored in the springs.
First, let's calculate the potential energy gained by the box as it falls:
Potential Energy = mass * gravity * height
Potential Energy = 10 kg * 9.8 m/s^2 * 0.5 m
Potential Energy = 49 J
Since the box is dropped, the potential energy is converted into potential energy stored in the springs.
The potential energy stored in a spring can be calculated using the equation:
Potential Energy = 0.5 * k * x^2
Where:
k = spring stiffness (250 N/m)
x = displacement of the spring from its equilibrium position
We need to solve for x (displacement) in this equation. When the maximum potential energy is stored in the springs, the displacement is also at its maximum, which we need to determine. Let's rearrange the equation and solve for x:
49 J = 0.5 * 250 N/m * x^2
x^2 = (49 J) / (0.5 * 250 N/m)
x^2 = 0.392 m^2
x = √(0.392 m^2)
x ≈ 0.626 m
Therefore, the maximum vertical displacement (d) of the pan is approximately 0.626 m.