A 4.40kg block hangs from a spring with spring constant 2160N/m . The block is pulled down 4.60cm from the equilibrium position and given an initial velocity of 1.40m/s back toward equilibrium.
What is the frequency of motion?
What is the amplitude?
What is the total mechanical energy of motion?
To find the frequency of motion, we can use the equation:
f = (1 / (2π)) * √(k / m)
where f is the frequency, k is the spring constant, and m is the mass of the block.
First, let's convert the displacement from centimeters to meters:
d = 4.60 cm = 0.046 m
Next, we can calculate the frequency using the formula:
f = (1 / (2π)) * √(k / m)
= (1 / (2π)) * √(2160 N/m / 4.40 kg)
= (1 / (2π)) * √(490.91 N/m)
= (1 / (2π)) * 22.14 Hz
So, the frequency of motion is approximately 3.52 Hz.
To find the amplitude of motion, we can use the given displacement:
Amplitude = |d|
Since the block is pulled down, the amplitude is given by:
Amplitude = 0.046 m
Therefore, the amplitude of motion is 0.046 m.
To calculate the total mechanical energy of motion, we can use the equation:
E = (1 / 2) * k * A^2
where E is the total mechanical energy, k is the spring constant, and A is the amplitude of motion.
Plugging in the values, we get:
E = (1 / 2) * 2160 N/m * (0.046 m)^2
= (1 / 2) * 2160 N/m * 0.002116 m^2
= 2.310 J
Therefore, the total mechanical energy of motion is approximately 2.310 Joules.