Terminal Velocity Given Acceleration at Instantaneous Velocity

In summary, the conversation is about finding the terminal velocity of a steel ball that is dropped from a large height, given the information that drag is proportional to velocity and when v = 20 m/s, a = 7.35 m/s^2. The relevant equation is ma = mg - kv, and the attempt at a solution involved substituting known values and solving for k. The final answer is 40 m/s, and there is some discussion about when to use v or v^2 in these types of problems.
  • #1
Greatness
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0

Homework Statement


This is a repost of a homework like question. The previous thread I did not understand.
In the assumption that drag is proportional to velocity, and when v = 20 m/s, a = 7.35 m/s^2, find the terminal velocity.

Homework Equations


The thread stated that the equation most relevant would be ma = mg - kv.

The Attempt at a Solution


I substituted all know values to make m(7.35) = m(9.8) - k(20), and attempted to solve, but the answer is 40 m/s.
 
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  • #2
How far did you get? Did you get stuck anywhere? It is too soon to give a hint, not enough has been done.
 
  • #3
verty said:
How far did you get? Did you get stuck anywhere? It is too soon to give a hint, not enough has been done.
None of that information is needed. The initial question is that it is dropped from a large height. The only information given is the information proveded (v and a).
 
  • #4
Never mind. I solved it by not replacing ma with 0 but by dividing by m first and replacing v with v^2.

In these types of problems, when is v or v^2 used?
 
  • #5

1. What is terminal velocity?

Terminal velocity is the maximum constant speed reached by a falling object when the downward force of gravity is equal to the upward force of air resistance. At this point, the object no longer accelerates and continues to fall at a constant speed.

2. How is terminal velocity calculated?

To calculate terminal velocity, you need to know the acceleration due to gravity (9.8 m/s²) and the drag coefficient of the object. By setting the downward force of gravity equal to the upward force of air resistance, you can solve for the object's maximum speed.

3. What is the relationship between acceleration and terminal velocity?

Acceleration is the rate of change of velocity, while terminal velocity is the maximum constant speed an object can reach. In the case of an object falling due to gravity, the acceleration will decrease as the object approaches terminal velocity.

4. Can terminal velocity change?

Yes, terminal velocity can change depending on the external factors such as air density, temperature, and the shape or size of the object. For example, a larger object will have a higher terminal velocity than a smaller object due to increased air resistance.

5. How does air resistance impact terminal velocity?

Air resistance, also known as drag, is a force that opposes the motion of an object through the air. As an object falls, air resistance increases until it becomes equal to the force of gravity, resulting in terminal velocity. A larger surface area or lower density of an object will increase air resistance and thus lower its terminal velocity.

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