Maths (M1) Friction,and Newton's Laws

Hi i'm struggling with this question, I know the method but it's not getting the correct answer.

Two particles P and Q of mass 4kg and 6KG respectively are joined by a light inextensible string. Particles are at rest on a rough plane. Coefficient of friction between particle and plane is 0.3. Force of 40N is then applied.

P (4kg)_________Q(6kg) 40N->

show that acceleration is 1.06 ms-2.

I have two equations I formed on each particle, and Tension is positive for Q and negative for P. I tried doing simultaneous but i got 2.12 acceleration rather than 1.06 which is why I'm puzzled. Any help/suggestions?

Reply 1

pineneedles

14

Original post by Xphoenix

Hi i'm struggling with this question, I know the method but it's not getting the correct answer.

Two particles P and Q of mass 4kg and 6KG respectively are joined by a light inextensible string. Particles are at rest on a rough plane. Coefficient of friction between particle and plane is 0.3. Force of 40N is then applied.

P (4kg)_________Q(6kg) 40N->

show that acceleration is 1.06 ms-2.

I have two equations I formed on each particle, and Tension is positive for Q and negative for P. I tried doing simultaneous but i got 2.12 acceleration rather than 1.06 which is why I'm puzzled. Any help/suggestions?

I got 1.06, can you show us what you did?
I modelled the two particles as one, and worked it out from there.

Reply 2

Xphoenix

OP

18

Original post by pineneedles

I got 1.06, can you show us what you did?
I modelled the two particles as one, and worked it out from there.

equations=
40-29.4-T=6A
40-29.4 +T= 4A

Simultaneous equations:
so 80-58.8=10a
so a= 2.12

I know that 2.12 is 2x bigger than 1.06 so maybe it's something to do with that?

Reply 3

pineneedles

14

Original post by Xphoenix

equations=
40-29.4-T=6A
40-29.4 +T= 4A

Simultaneous equations:
so 80-58.8=10a
so a= 2.12

I know that 2.12 is 2x bigger than 1.06 so maybe it's something to do with that?

I think it's because you've taken the 40 N force into account with the 4 kg particle when you shouldn't have. The tension in the string is the force which is moving the 4kg particle, not the 40 N force.

For P (4kg) :
T - 11.76 = 4A
40 - T - 17.64 = 6A
40 - 29.4 = 10A
10.6 = 10A
A = 1.06

Alternatively, it's quicker to model them as one particle. You can do this because the string is inextensible and because the particles are connected, they have the same acceleration.

F = ma
40 - (0.3 * 10g) / 10 = 1.06

Maths (M1) Friction,and Newton's Laws

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