Question about forces over time

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  • Thread starter Thread starter Mr Davis 97
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    Forces Time
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Discussion Overview

The discussion revolves around understanding the application of forces over time, particularly in the context of Newton's second law (F = ma) and its implications for acceleration and motion. Participants explore how time intervals affect the resulting acceleration and velocity of objects subjected to forces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to apply Newton's second law when considering forces over time, questioning how to determine acceleration when a force is applied for a specific duration.
  • Another participant asserts that while F = ma relates instantaneous values, it does not directly address the effects of time on acceleration.
  • A different viewpoint suggests that acceleration can be derived from the change in velocity over time, leading to a reformulation of the force equation as f = m * (vc / t), where vc represents the change in velocity.
  • One participant mentions that to find the resulting acceleration, one can use a = f/m, but emphasizes the need for additional equations to determine velocity or distance after a time interval, referencing the SUVAT equations for uniform acceleration.
  • There is a side note questioning whether an acceleration of 2 m/s² is correct when a force of 4 N is applied to a 2 kg box, which another participant confirms as correct.
  • Participants discuss how the duration of force application affects the final velocity, noting that while the acceleration remains constant, the velocity changes depending on how long the force is applied.
  • One participant introduces the concept of impulse, stating that the product of constant force and time equals the change in momentum.

Areas of Agreement / Disagreement

Participants generally agree on the application of Newton's second law and the concept of acceleration, but there is no consensus on how to best incorporate time into these calculations. Multiple competing views on the relationship between force, time, and resulting motion remain present.

Contextual Notes

Some participants highlight the need for different equations to address questions about velocity and distance after a force has been applied, indicating that the discussion may be limited by assumptions about uniform acceleration and the specific conditions of the problems posed.

Mr Davis 97
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I am a little confused about forces when time is considered. I understand the nature of forces, ie that they are a push or a pull and that they induce a change in momentum and thus an acceleration. However, my question is, how could we solve such a problem as "If a force of 2 N is applied to a 4 kg block for 6 seconds, what is the resulting acceleration?" When solving force problems, we usually always refer to Newton's second law, F = ma, but I do not see how this equation helps solving problems that involve the application of force over a time interval.

As a side note, if given a problem such as "If a force of 4 N is applied to a 2 kg box, what is the resulting acceleration?" Is 2 m/s^2 really the correct answer? What if we apply the 4 N for 0.5 s rather than 0.1 s? How does F = ma take this into account?
 
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Mr Davis 97 said:
F = ma, but I do not see how this equation helps solving problems that involve the application of force over a time interval.
It doesn't. It relates instantaneous values at some time point.

Mr Davis 97 said:
However, my question is, how could we solve such a problem as "If a force of 2 N is applied to a 4 kg block for 6 seconds, what is the resulting acceleration?
The acceleration is constant 0.5m/s^2 during those 6s. You can use the time to find the change in velocity and position.
 
If you consider Newtons f = m * a
But a ( acceleration ) = velocity change (vc) / time
So you get:
f = m * ( vc / t )
vc is what you want
 
Mr Davis 97 said:
I am a little confused about forces when time is considered. I understand the nature of forces, ie that they are a push or a pull and that they induce a change in momentum and thus an acceleration. However, my question is, how could we solve such a problem as "If a force of 2 N is applied to a 4 kg block for 6 seconds, what is the resulting acceleration?" When solving force problems, we usually always refer to Newton's second law, F = ma, but I do not see how this equation helps solving problems that involve the application of force over a time interval.

You only need a=f/m to calculate the resulting acceleration. However part 2 might ask "How fast is it going after 6 seconds?" or "how far has it traveled after 10 seconds"? For that you need different equations. In my school days we learned the SUVAT equations of motion which are mentioned in here..

http://en.wikipedia.org/wiki/Equations_of_motion#Uniform_acceleration

They apply to situations where the acceleration is uniform (constant).
 
Mr Davis 97 said:
As a side note, if given a problem such as "If a force of 4 N is applied to a 2 kg box, what is the resulting acceleration?" Is 2 m/s^2 really the correct answer?

Yes.

What if we apply the 4 N for 0.5 s rather than 0.1 s? How does F = ma take this into account?

The acceleration will be 2m/s^2 in both cases. However it only continues to accelerate for as long as the force is applied. If the force stops the object will stop accelerating and will then coast along at whatever velocity it had achieved when the force stopped. One of the SUVAT equations is...

V = U + at
where
V = final velocity
U = initial velocity (zero)
a = acceleration
t = time

So if the force is applied for 0.1 seconds the velocity V is...

V = 0 + 2*0.1
= 0.2m/s

If the force is applied for 0.5 seconds the final velocity is

V = 0 + 2*0.5
= 1m/s
 
Its interesting to note that the impulse ( ( constant ) force * time ) = the momentum change.
 

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