Will the acceleration of two particles be different with a rough surface?

In summary, the conversation discusses the approach to finding the acceleration and tension in a system of two particles on a rough surface. The participants consider combining the masses and friction forces, as well as using separate free body diagrams for each mass. They ultimately come to a correct equation for acceleration and tension, taking into account the individual masses and forces.
  • #1
Jadenag
33
0
27zbsjt.jpg


I need help with part c. Since there is now a rough surface does that mean the acceleration of the two particles will be different? Is it wrong to simply add up the two masses and pretend that its one mass. And then find the net friction force and use f=ma directly?
I don't understand in which cases I have to consider the two particles as one and in which cases separately?
 
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  • #2
Jadenag said:
27zbsjt.jpg


I need help with part c. Since there is now a rough surface does that mean the acceleration of the two particles will be different? Is it wrong to simply add up the two masses and pretend that its one mass. And then find the net friction force and use f=ma directly?
I don't understand in which cases I have to consider the two particles as one and in which cases separately?

No problem with considering them together when convenient.

Consider the combined mass and the combined friction in connection with the applied force, F, to find the acceleration.
Then use the Tension, the friction force on m2 the mass of m2 and the acceleration to find the value of T.
 
  • #3
PeterO said:
No problem with considering them together when convenient.

Consider the combined mass and the combined friction in connection with the applied force, F, to find the acceleration.
Then use the Tension, the friction force on m2 the mass of m2 and the acceleration to find the value of T.

I find the acceleration to be
a= [F-μ(m1+m2)g]/m1

Couldnt I also get another equation for a?

/e
Are you suggesting I use this a and put it in f=ma for m2?
Also since I can make FBD for either of the two masses and hence i could get two different equations for a. but both would be correct right?
 
  • #4
Jadenag said:
I find the acceleration to be
a= [F-μ(m1+m2)g]/m1

Couldnt I also get another equation for a?

You are using a = F/m

I like your force [accounting for the friction on both masses]

I don't like your mass so much, as you have used only m1, rather than the combined mass.
 
  • #5
PeterO said:
You are using a = F/m

I like your force [accounting for the friction on both masses]

I don't like your mass so much, as you have used only m1, rather than the combined mass.

oh god. lol. sorry yes. the denominator should have the sum of the two masses. now how to approach the T
so this means there's only one correct equation for a. xd
 
  • #6
Jadenag said:
oh god. lol. sorry yes. the denominator should have the sum of the two masses. now how to approach the T

having found a, now consider only mass m2 as T is the force that accelerates it.
This time you do only consider just one mass.
 
  • #7
PeterO said:
having found a, now consider only mass m2 as T is the force that accelerates it.
This time you do only consider just one mass.

Considering m2

T-Ff=m2a
T-μm2g=m2a

a= [F-μ(m1+m2)g]/(m1+m2)

Hence:
T= μm2g + m2[F-μ(m1+m2)g]/(m1+m2)

Hope I got it and typed it correct too. Thankyou for the help!
 

FAQ: Will the acceleration of two particles be different with a rough surface?

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