How to Determine the Mass of Bananas Using a Spring Scale

[Boxlife27]

Homework Statement

At an outdoor market, a bunch of bananas is
set on a spring scale to measure the weight.
The spring sets the full bunch of bananas into
vertical oscillatory motion, which is harmonic
with an amplitude 0.14 m. The maximum
speed of the bananas is observed to be 2 m/s.
What is the mass of the bananas? The
spring of the scale has a force constant
523 N/m.

Homework Equations

The equations I have learned are Hooke's Law (-kx=F) and period of a spring = T = 2pi sqrt(m/k)

The Attempt at a Solution

I have tried to solve this problem, but I'm not sure how I can use the amplitude and velocity to determine the period, which I would then use to find mass. THANK YOU

 

[SammyS]

Homework Statement

At an outdoor market, a bunch of bananas is
set on a spring scale to measure the weight.
The spring sets the full bunch of bananas into
vertical oscillatory motion, which is harmonic
with an amplitude 0.14 m. The maximum
speed of the bananas is observed to be 2 m/s.
What is the mass of the bananas? The
spring of the scale has a force constant
523 N/m.

Homework Equations

The equations I have learned are Hooke's Law (-kx=F) and period of a spring = T = 2pi sqrt(m/k)

The Attempt at a Solution

I have tried to solve this problem, but I'm not sure how I can use the amplitude and velocity to determine the period, which I would then use to find mass. THANK YOU

Start by writing an expression for the vertical position of the bananas as a function of time. Let A = the amplitude.

 

[Boxlife27]

Thanks. So, f(t) = (2m/s) (.14) to find the time? Something like this?

 

[SammyS]

Thanks. So, f(t) = (2m/s) (.14) to find the time? Something like this?

No.

f(t) is sinusoidal.

You don't know the amplitude at this point, so call it A or something.

 

[Boxlife27]

Sorry, I'm only a soph in high school, barely taken trigonometry. Would you explain this a bit more, please? Thank you

 

[AlephZero]

Homework Equations

The equations I have learned are Hooke's Law (-kx=F) and period of a spring = T = 2pi sqrt(m/k)

What about the formulas for the maximum velocity and acceleration in simple harmonic motion, given the amplitude and the frequency? (You don't need the acceleration formula, for this question).

Sammy S is trying to get you to derive those formulas yourself using trig, but they are probably in your textbook.

 

[Boxlife27]

Thank you both. Would I use the equation
Vmax = xMax * sqrt (k/mass)?

 

[Boxlife27]

Yes! I just entered the answer and it is correct. Thank you both.

 

[SammyS]

Yes! I just entered the answer and it is correct. Thank you both.

Yup!

Good !