Laws of motion problem

  • Thread starter coldblood
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  • #1
coldblood
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Hi friends, The problem is from Newton's Laws.

The problem is as follows:
https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-ash4/1006364_1417581381802301_666606151_n.jpg

IInd law states,
Force, F = dP/dt
=> F = d(mv)/ dt

Out come,

If m is constant, v is variable, F = m.[d(v)/dt] => F = m.a

If v is constant, m is variable, F = v.[d(m)/dt] => F = v.[rate of change of mass]

If both m and v are variable, F = m.[d(v)/dt] + v.[d(m)/dt]

Hence the answer of the question should be Option (B). But the book states that answer is option (C) is correct. How is it so.

Please friends help me in solving this issue.

Thank you all in advance. I would appreciate the help.
 

Answers and Replies

  • #2
Basic_Physics
358
6
[itex]\vec{v}[/itex] is a variable. It is the instantaneous velocity at all times. So [itex]\vec{a}[/itex]=[itex]\frac{d\vec{v}}{dt}[/itex]. [itex]\lambda[/itex] is the constant rate at which sand is leaking out. So the amount of mass that would be lost after a period t would be [itex]\lambda[/itex]t.
 
  • #3
coldblood
133
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[itex]\vec{v}[/itex] is a variable. It is the instantaneous velocity at all times. So [itex]\vec{a}[/itex]=[itex]\frac{d\vec{v}}{dt}[/itex]. [itex]\lambda[/itex] is the constant rate at which sand is leaking out. So the amount of mass that would be lost after a period t would be [itex]\lambda[/itex]t.

So why not Option (B) is correct?
 
  • #4
Basic_Physics
358
6
In your last step where you assume that both m and v are variable you should actually use partial differentiation, not ordinary differentiation.
 
  • #5
arildno
Science Advisor
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Rewrite your original post with non-psychotic letters, please.
 
  • #6
Basic_Physics
358
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In applying the product rule the first mass will also be m not mo as in answer B.
 
  • #7
lendav_rott
224
10
I did that problem over and over and concluded that option C is correct and please, I half had a seizure reading the 1st post :/
 
  • #8
coldblood
133
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Thank you all friends. The problem has been cleared. A apologize for the bad fonts.
 

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