Christine Karera hangs a spring and it oscillates at a frequency of 60 cycles in a minute when an object is attached to it. Calculate the mass of the object if the spring constant is 250 N/m.
To calculate the mass of the object attached to the spring, we can use the formula for the frequency of oscillation of a mass-spring system:
f = 1 / (2π) * √(k / m)
Where:
f = Frequency of oscillation (in cycles per second)
k = Spring constant (in Newtons per meter)
m = Mass of the object (in kilograms)
First, let's convert the frequency from cycles per minute to cycles per second since the formula requires frequency in cycles per second.
Given:
Frequency (f) = 60 cycles per minute
To convert cycles per minute to cycles per second, we divide by 60:
f = 60 cycles per minute / 60 seconds = 1 cycle per second
Now we can rearrange the formula to solve for the mass, m:
m = k / (4π² * f²)
Given:
k = 250 N/m
f = 1 cycle per second
Plugging the values into the formula:
m = 250 N/m / (4π² * (1 cycle per second)²)
Simplifying:
m = 250 N/m / (4π² * 1²)
m = 250 N/m / (4π²)
m = 250 / (4 * 3.14²)
m ≈ 5.04 kg
Therefore, the mass of the object attached to the spring is approximately 5.04 kilograms.