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$\bullet$$\bullet$ Two crates connected by a rope of negligible mass lie ona horizontal surface. (See Figure $5.53 .$ ) Crate $A$ has mass $m_{A}$and crate $B$ has mass $m_{B}$ . The coefficient of kinetic frictionbetween each crate and the surface is $\mu_{k .}$ The crates arepulled to the right at a constant velocity of 3.20 $\mathrm{cm} / \mathrm{s}$ by ahorizontal force $\vec{\boldsymbol{F}} .$ In terms of $m_{A}, m_{B},$ and $\mu_{\mathrm{k}},$ calculate(a) the magnitude of the force $\vec{\boldsymbol{F}}$ and (b) the tension in therope connecting the blocks. Include the free-body diagram ordiagrams you used to determine each answer.

a) $\mu_{\mathrm{k}}\left(m_{\mathrm{A}}+m_{\mathrm{B}}\right) g$\b) $\mu_{\mathrm{k}} m_{\mathrm{A}} g$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Michigan - Ann Arbor

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our first note that constant ah, velocity for each crate means that acceleration is zero. And so they are. Ah, equilibrium. And so let's just let's draw out the free body diagrams for about crates. And so for create air. We have obviously the force of gravity acting downwards. Mason, she and you, the normal force exerted about floor on create a And someday you have tension from the wire acting too. Right. And you have, uh, fiction forests calling absolutely a opposing that. Okay. And for Craig B, you have force of gravity and subi times G act downwards. You have normal force on D B, exerted by the floor acting upwards. You have tension acting to the left. This is the Newton's second law pair Also have force of us our friction force on B s, A. B acting to the left, and you have finally the force applied Force f acting to the right. Okay, these free body diagrams we have are set up. So now, uh, really, where we have to do is use Newton's second law vehicles. So let's first resolve forces in the white direction and net force will be zero in both cases, for and B And so you have and severe equals m severe times. She and similarly and Subi recalls and said be times she because normal force is just equal to wait in both for both crates. Okay, now in the wind direction Oh, are are in the extraction I should say again you have no met the Met forests that zero and what that means is three minus have some air will be zero And so tea will be cold to absent And remember the force of fiction. And she's given by the coefficient of kinetic friction times the, uh, times the normal force. So from UK time sensible and similarly for B, you have tea. Now you have t plus the Friction Force, which is a call to the Applied Force F. And so this case t will be f minus. Have some B and that's ah just means of care times. And so be much like over here. Okay, so let's call this first equation for tea version one on the second equation for two equation two. Okay. And let's remember that these air that the normal force is just equal to the weight. So what we get is S O. We sent one. He called it to their just equations for tea. Now we get music K Times and today he calls It's big, big, half minus music care terms and subi. And so big half the force applied is music care times and someday plus answer B and noting that they're just the weight's off cards and B creates A and B. We have that afters music, K times, and so eventually the rate of create and plus absolute beauty with a B so that could be further simplified to new carrot and she times may possibly be. That's here for us and Part B. We already implicitly did what It's the tension. Tension is from Equation one. I have tension is Mrs Kerr Times and and so that's just missing care. Time's a tanski and that's it.

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