A vertical scale on a spring balance reads from 0 to 220N . The scale has a length of 15.0cm from the 0 to 220N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.45Hz .
Part A
Ignoring the mass of the spring, what is the mass m of the fish?
To find the mass of the fish, we can use the equation for the period of a mass-spring system.
The period (T) is the time it takes for one complete oscillation or cycle. It is related to the frequency (f) by the equation T = 1/f.
In this case, the frequency is given as 2.45 Hz. We can substitute this value into the equation to find the period:
T = 1/2.45 Hz
Next, we need to find the angular frequency (ω) of the spring-mass system. This can be calculated with the formula ω = 2πf, where f is the frequency.
ω = 2π × 2.45 Hz
Having obtained the angular frequency, we can use it to calculate the mass of the fish. The equation for the period of a mass-spring system is given by:
T = 2π√(m/k)
Where m is the mass and k is the spring constant. However, in this case, we are instructed to ignore the mass of the spring, so we can simplify the equation to:
T = 2π√(m/g)
Where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Rearranging the equation to solve for m, we have:
m = (T/(2π))^2 × g
Substituting the value of T we found earlier, and the value of g, we get:
m = ((1/2.45)/(2π))^2 × 9.8 m/s^2
Now we just need to calculate this value to find the mass of the fish.