A spring stretches 4.3 cm when a 13 g object is hung from it. The object is replaced with a block of mass 22 g that oscillates in simple harmonic motion, calculate the period of motion.
To calculate the period of motion for the block, we need to use Hooke's Law, which relates the period of oscillation to the mass and the spring constant.
First, let's calculate the spring constant (k) using Hooke's Law formula:
F = k * x
Where:
F is the force applied to the spring (weight of the object)
k is the spring constant
x is the displacement of the spring (stretching or compression)
Given that the object has a mass of 13 g and stretches the spring by 4.3 cm (0.043 m), we can calculate the force applied to the spring:
F = m * g
F = 0.013 kg * 9.8 m/s^2
F ≈ 0.1274 N
Now we can use Hooke's Law to find the spring constant:
k = F / x
k = 0.1274 N / 0.043 m
k ≈ 2.968 N/m
Now that we have the spring constant, we can calculate the period of motion using the formula:
T = 2π * √(m / k)
Where:
T is the period of motion
m is the mass of the block
k is the spring constant
Given that the block has a mass of 22 g (0.022 kg), we can substitute the values into the formula:
T = 2π * √(0.022 kg / 2.968 N/m)
T ≈ 0.876 seconds
Therefore, the period of motion for the block is approximately 0.876 seconds.