Relationship between Velocity, Kinetic Energy and Mass

In summary, the conversation revolves around the relationship between velocity, mass, and force in a system with constant acceleration. The equations F=ma=mv/t and E=mv2/2 are discussed and it is concluded that the final velocity is inversely proportional to the mass. Alternative routes to calculating the final velocity are also explored.
  • #1

Homework Statement


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Homework Equations


i) F=ma=mv/t
ii) E=mv2/2

The Attempt at a Solution


Now based on equation 1 , I have concluded that the velocity gained is inversely proportional to m, and that so is the kinetic energy , I have seen otherwise.[/B]
 
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  • #2
How can you conclude that if equation 1 does not contain any distance/displacement at alll ? You need other equations !
 
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  • #3
BvU said:
How can you conclude that if equation 1 does not contain any distance/displacement at alll ? You need other equations !
Oh hmmmm, x=at^2/2, which means, a=2x/t^2, which means that mv/t=2mx/t^2=F, so does this mean they are independent , I am sorry , I am a little weak.Could you please elaborate?
 
  • #4
mv/t = F doesn't help you if you don't know how t depends on m.

Would the exercise be easier for you if the text would read:

You have a force ##F## to accelerate a mass ##m## from rest with constant acceleration over a distance ##d##. What is the final velocity ?​
 
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  • #5
BvU said:
mv/t = F doesn't help you if you don't know how t depends on m.

Would the exercise be easier for you if the text would read:

You have a force ##F## to accelerate a mass ##m## from rest with constant acceleration over a distance ##d##. What is the final velocity ?​
I think I see something , the energy gained by the system would be Fd=mad, so this implies that mv^2/2=mad, v^2/2=ad, so this would mean the kinetic energy is independent of m ? Further a=F/m , v=sqrroot(Fd/m), does that mean v varies in an inverse proportion with sqrt(m)
 
  • #6
BvU said:
mv/t = F doesn't help you if you don't know how t depends on m.

Would the exercise be easier for you if the text would read:

You have a force ##F## to accelerate a mass ##m## from rest with constant acceleration over a distance ##d##. What is the final velocity ?​
Sir ?
 
  • #7
Nile Anderson said:
kinetic energy is independent of m
Correct
Nile Anderson said:
Further a=F/m , v=sqrroot(Fd/m), does that mean v varies in an inverse proportion with sqrt(m)
Bingo.

Can you also do the alternative route ? ## \ d = {1\over 2} at^2\ ## tells you ##\ t \propto \sqrt d\ ## and you already had ##\ mv/t = F ##
 
  • #8
BvU said:
Correct
Bingo.

Can you also do the alternative route ? ##\ d = {1\over 2} at^2} \ ## tells you ##\ t \propto \sqrt d\ ## and you already had ##\ mv/t = F ##
Thank you so much sir , I get it now
 
  • #9
BvU said:
Correct
Bingo.

Can you also do the alternative route ? ## \ d = {1\over 2} at^2\ ## tells you ##\ t \propto \sqrt d\ ## and you already had ##\ mv/t = F ##
Hmmmmm
 
  • #10
Right , I get back the same place sir, thank you so much sir , that helped alot.
 
  • #11
Hmmm as in "delicious" or Hmmm as in "I don't believe a word of what I read" :smile: ?
 
  • #12
BvU said:
Hmmm as in "delicious" or Hmmm as in "I don't believe a word of what I read" :smile: ?
lol "hmmm" as in intriguing
 
  • #13
Nile Anderson said:
Right , I get back the same place sir, thank you so much sir , that helped alot.
Ah, posts crossed. Well done. On to the next exercise.

PS
You have a force ##F## to accelerate a mass ##m## from rest with constant acceleration over a distance ##d##. What is the final velocity ?​
was meant to seduce you to calculate v as a function of knowns:
$$\ d = {1\over 2} at^2\ \Rightarrow t = \sqrt{2d\over a} \Rightarrow v = at = {F\over m} \sqrt{2dm\over F} \Rightarrow v\propto 1/\sqrt m$$
 

1. What is the relationship between velocity and kinetic energy?

The relationship between velocity and kinetic energy can be described by the equation KE = 1/2 * mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity. This equation shows that kinetic energy is directly proportional to the square of the velocity, meaning that as velocity increases, kinetic energy increases exponentially.

2. How does mass affect kinetic energy?

Mass has a direct relationship with kinetic energy, as shown in the equation KE = 1/2 * mv^2. This means that as mass increases, so does kinetic energy. However, the effect of mass is not as significant as the effect of velocity on kinetic energy.

3. Can kinetic energy be negative?

No, kinetic energy cannot be negative. By definition, kinetic energy is the energy an object possesses due to its motion, and motion cannot have a negative value. Therefore, kinetic energy is always a positive value.

4. How does velocity affect the relationship between mass and kinetic energy?

Velocity plays a crucial role in the relationship between mass and kinetic energy. As mentioned earlier, kinetic energy is directly proportional to the square of velocity. This means that even a slight increase in velocity can have a significant impact on the overall kinetic energy, even with a constant mass.

5. What is the unit of measurement for kinetic energy?

The unit of measurement for kinetic energy is joules (J). This is the same unit used to measure other forms of energy, such as potential energy and work.

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