HOW DO YOU DO THIS PHYSICS PROBLEM
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HOW DO YOU DO THIS PHYSICS PROBLEM

[From: ] [author: ] [Date: 11-11-02] [Hit: ]
We need to consider the potential energy stored in the spring when it is stretched or compressed to its maximum (2.7 cm or 0.027 cm).The grapes will have their maximum velocity when the spring passes its equilibrium point (x = 0),So........
A bunch of grapes is placed in a spring scale at a supermarket. The grapes oscillate up and down with a period of 0.43 s.


What is the maximum speed of the grapes if their amplitude of oscillation is 2.7 cm?
Vmax=_____m/s




thanks

-
The system approximates a simple harmonic oscillator, so we'll start with the period equation:

T = 2π√(m/k)

Where m is the mass of the grapes (assuming the spring is massless) and k is the spring constant. Since we don't know either of these values, we cannot completely solve this problem yet, but we can get a ratio:

0.43 s = 2π√(m/k)

0.0684 s = √(m/k)

m/k = 0.00468 s²

So the mass to spring constant ratio is 0.00468 s².

m = (0.00468 s²)k

We need to consider the potential energy stored in the spring when it is stretched or compressed to its maximum (2.7 cm or 0.027 cm).

Us = 1/2 kx²

The grapes will have their maximum velocity when the spring passes its equilibrium point (x = 0), at which point:

K = 1/2 mv²

So...

1/2 kx² = 1/2 mv²

Keeping in mind that m = (0.00468 s²)k

1/2 k(0.027 m)² = 1/2 (0.00468 s²)k v²

(3.645e-4 m²)k = (0.00234 s²)k v²

Divide k out of both sides:

(3.645e-4 m²) = (0.00234 s²) v²

v² = 0.156 m²/s²

v = 0.395 m/s

I hope that helps. Good luck!
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