Solving a Physics Problem: Calculating Maximum Distance for Falling Fish

In summary, the fish stretches the spring by an amount d. The maximum distance the spring stretches is equal to the mass of the fish multiplied by the force constant of the spring.
  • #1
pedro_infante
7
0

Homework Statement


If a fish is attached to a vertical spring and slowly lowered to its equilibrium position, it is found to stretch the spring by an amount d.
If the same fish is attached to the end of the unstretched spring and then allowed to fall from rest, through what maximum distance does it stretch the spring? (Hint: Calculate the force constant of the spring in terms of the distance d and the mass m of the fish.)

Homework Equations


F=-kx

The Attempt at a Solution


I do not remember my prof doing anything like this in class. Can anyone help?
 
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  • #2


In this case, you need to use the conservation of energy principle. Do you know the equation for the energy in a compressed/extended spring?
 
  • #3


yeah I just don't know where to start really. it's F=-kx
 
  • #4


hint: what's the force provided by the fish?

how would i go about getting k after I have found F and x...

I have a feeling you are missing something in your problem statement...
 
  • #5


well that's all the mastering physics website states as the problem statement.
so F=ma so F= mg
so mg=-kx
so k=mg/x?
 
  • #6


yes, and now you need the equation for the energy in a compressed/extended spring.
 
  • #7


pedro_infante said:
well that's all the mastering physics website states as the problem statement.
so F=ma so F= mg
so mg=-kx
so k=mg/x?

In your case,
sumF=mg-kx=0
at x=d, mg=kd --> k=mg/d

To find the maximum distance the spring stretches, you need to use an energy perspective (@Chi Meson)

sum E=mgx-(k*x^2)/2-(m*v^2)/2=0
The first term is the potential energy of the mass.
The second term is the potential energy of the spring.
The third term is the kinetic energy of the mass (These problems ignore the kinetic energy of the spring).

Solve the energy equation for x.
Hint: When the spring is at its maximum stretch, what is your velocity v?
 

1. How do you calculate the maximum distance for a falling fish?

To calculate the maximum distance for a falling fish, you will need to use the kinematic equation for displacement, which is:
d = vi*t + (1/2)*a*t^2
Where d is the maximum distance, vi is the initial velocity (usually 0 for a falling object), t is the time, and a is the acceleration due to gravity (9.8 m/s^2).

2. What information do I need to know in order to calculate the maximum distance for a falling fish?

In order to calculate the maximum distance for a falling fish, you will need to know the initial velocity of the fish (usually 0 for a falling object), the time that it takes for the fish to fall, and the acceleration due to gravity (9.8 m/s^2).

3. Is the maximum distance affected by the mass of the fish?

Yes, the maximum distance for a falling fish is affected by the mass of the fish. This is because the acceleration due to gravity, which is a factor in the calculation, is affected by the mass of the object. Heavier objects will experience a greater force of gravity and therefore will fall faster and farther.

4. Can I use the same equation to calculate the maximum distance for objects of different shapes?

Yes, you can use the same equation to calculate the maximum distance for objects of different shapes. As long as you know the initial velocity, time, and acceleration due to gravity, you can use this equation to calculate the maximum distance for any object falling under the influence of gravity.

5. How can I use the calculation for maximum distance to predict the landing spot of a falling fish?

To predict the landing spot of a falling fish, you can use the calculation for maximum distance to determine how far the fish will fall from its initial starting point. This can be helpful for fishermen or researchers studying the behavior of fish in water bodies. Keep in mind that other factors, such as air resistance and wind, may also affect the actual landing spot of the fish.

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