Classical mechanics: Force versus time graph

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Homework Statement


force_vs_time_graph.png

A particle of mass m=4.0 kg is moving along the x-axis. The particle is being acted upon by a variable single force F⃗ , directed along the x-axis. At t=0 s, the particle is moving at v_0=−3 m/s.

What is the first time t>0 when the particle comes to a stop momentarily?

The Attempt at a Solution


because I know the initial velocity ,I know the initial momentum and I know the final momentum too(as the particle stops temporarily) but the force is variable otherwise I would have equated change in momentum to the impulse imparted.and found the time t.

what should I do?
 

Answers and Replies

  • #2
gneill
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What does area under a Force vs Time curve represent?
 
  • #3
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What does area under a Force vs Time curve represent?

it represents impulse.

##mv_f-mv_i=J##
##0-m(-3)=∫F. dt##
 
  • #4
cnh1995
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it represents impulse.

##mv_f-mv_i=J##
##0-m(-3)=∫F. dt##
So you'll have to calculate the value of t at which the area of the curve becomes 12.
 
Last edited:
  • #5
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So you'll have to calculate the value of t at which the area of the curve becomes 12.

how will I do it? I don't have the force as a fn of time.
 
  • #6
cnh1995
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I don't have the force as a fn of time.
You do.
ses.edx.org%2Fasset-v1%3AMITx%2B8.MechCx_2%2B2T2015%2Btype%40asset%2Bblock%2Fforce_vs_time_graph.png

First you need to formulate F as a function of time between various intervals.
 
  • #7
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you need to formulate F as a function of time between various intervals.

you mean from 0 to 1 sec its 2.5
from 1 to 4 its 12

but the answer is 3.375
 
  • #8
cnh1995
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answer is 3.375
Indeed it is. That's the final answer.
you mean from 0 to 1 sec its 2.5
from 1 to 4 its 12
No. From t=0 to t=1, what is F(t) and so on..
 
  • #9
cnh1995
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Indeed it is. That's the final answer.

No. From t=0 to t=1, what is F(t) and so on..
Ok right, if you are talking in terms of areas directly..
 
  • #10
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if you are talking in terms of areas directly..

area under the f/t curve is all I know what else are you saying.also I am fairly new to calculus
 
  • #11
cnh1995
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you mean from 0 to 1 sec its 2.5
from 1 to 4 its 12
Ok. So, from 0 to 4, the area is 14.5. So, t must be between 1 to 4. Agree? Because total area is 12 and out of that, 2.5 is already in between 0 to 1.
 
  • #12
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Ok. So, from 0 to 4, the area is 14.5. So, t must be between 1 to 4. Agree?

yes totally because of the areas.
 
  • #13
cnh1995
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yes totally because of the areas.
So, from t=1 to t=4, you need to find at what value of t will the area be 9.5(i.e. 12-2.5). Can you do it?
 
  • #14
cnh1995
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yes totally because of the areas.
You know its a rectangle from t=1 to t=4. You know the height. I believe the answer is in plain sight. Good luck..
 
  • #15
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answer is in plain sight

##∫F.dt+F_c(t-1)=-mv_i##
(the integral is form t=0 to t=1) (c means const)
## 2.5+4(t-1)=-4*(-3)##
##t=3.375##

@cnh1995
thank you
 

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