Two bodies m1 50 kg and m2 30 kg are in contact on a...

Two bodies, m₁ = 5.0 kg and m₂ = 3.0 kg, are in contact on a horizontal surface. The coefficient of kinetic friction between the surface and both bodies is μ₁ = 0.30. A force of F = 30.0 N is applied horizontally to body m₁, causing both bodies to move together. a) What is the acceleration of the system? b) What is the force of kinetic friction acting on each body?

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00:01 Looks like now we're starting to use friction.

00:04 So, draw this diagram again.

00:19 Okay, we're going to say that m1 is 10 kilograms.

00:27 M2 is 4k0.

00:33 Okay, the coefficient of friction between m1 and the horizontal surface is 0 .5.

00:57 Oh, and that static friction.

00:59 And then we've got kinetic friction.

01:02 I was wondering what they're going to talk about here.

01:05 Kinetic friction is 0 .3.

01:12 All right.

01:16 A, what will its acceleration be? so, we're going to draw a free body diagram of m1 and m2.

01:32 M2 is going to have tension here.

01:37 M2g here.

01:39 M1 is going to have tension here, friction here.

01:51 And then it's going to have m1g here and the normal force here, which makes the normal force m1g, which makes the friction force mu times the normal force, which is m1g.

02:16 So now, t minus mu m1g, summing the forces in the x direction, equals m1a.

02:29 Also, m2g minus t equals m2a.

02:38 Now, solving this for a, we get, i want to get t out of the equation.

02:57 So t on this side is going to be m2 times g minus a.

03:12 Substituting it into the other equation, okay? now trying to solve for a, so that's going to be m2 minus mu m1, g equals m1 plus m1.

03:47 M2a, just rearranging it...