At an outdoor market, a bunch of bananas
is set into oscillatory motion with an amplitude of 30.0781 cm on a spring with a spring constant of 15.7711 N/m. The mass of the bananas is 69.6297 kg.
What is the speed of the bananas?
Answer in units of m/s
To find the speed of the bananas, we need to use the formula for the speed of an object in simple harmonic motion (SHM):
v = Aω
Where:
v = speed of the object
A = amplitude of the motion
ω = angular frequency of the motion
To calculate the angular frequency (ω), we can use the formula:
ω = √(k/m)
Where:
k = spring constant
m = mass of the object
Let's calculate ω first:
ω = √(15.7711 N/m / 69.6297 kg)
= √(0.226216 N/kg)
≈ 0.475821 rad/s
Now, we can calculate the speed (v) using the amplitude (A) and ω:
v = (0.300781 m) * (0.475821 rad/s)
≈ 0.143056 m/s
Therefore, the speed of the bananas is approximately 0.143056 m/s.