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Two horizontal forces, $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2},$ arc acting on a box, but only $\overrightarrow{\mathbf{F}}_{1}$ is shown in the drawing. $\overrightarrow{\mathbf{F}}_{2}$ can point either to the right or to the left. The box moves only along the $x$ axis. There is no friction between the box and the surface. Suppose that $\overrightarrow{\mathbf{F}}_{1}=+9.0 \mathrm{N}$ and the mass of the box is 3.0 $\mathrm{kg}$ . Find the magnitude and direction of $\overrightarrow{\mathrm{F}}_{2}$ when the acceleration of the box is $(\mathrm{a})+5.0 \mathrm{m} / \mathrm{s}^{2}, \quad$ (b) $-5.0 \mathrm{m} / \mathrm{s}^{2},$ and $(\mathrm{c}) 0 \mathrm{m} / \mathrm{s}^{2}$

$+6 N$

$-24 N$

$-9.0 N$

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Numerade Educator

University of Washington

Simon Fraser University

University of Sheffield

in these questions we have to force is at one and two that is acting on his book. Then we do that. The magnitude of the four step one is the question. Nine new terms and it's pointing for the right we have now is over. What is the magnitude of the force at two. And we don't do what direction does the force at two points. So this he's just a guess, so we can start. So problem two. By writing down the new term second law for that box, you get the following, then that force on the box is Nikolas Truth, that one. What that's true, then the net force. Is it close to nine? What I have to. We don't know what is their value off at two. And then we know that the Net force is opposed to the match off the box kinds. Acceleration of the box uniform you're forced to. It's them equals to the mask off the box Times declaration off the box, minus nine. But we know what is the matter of the box Mass. Off the box is three kilograms. So after you, is it close to three times the acceleration minus nine. So on the first item, acceleration is given at five meters per second square. Then in the situation the Force F troop that is acting in the box in records to tree times five minus nine, which you're 15 minus nine and they gave us six. New comes So on the first item, the force, after his six new turns to the right. On the second item, we get on exploration off minus five meters per seconds. Where and then the force actu Well, b equals 23 times minus five minus nine. And this is the coast to minus 15 minus nine, which is because to minus 24 new terms. Therefore, in this situation at two, he's 24 new terms to the left. Why left? Because it has a negative sign here. And we have supposed that it was pointing to the right. So you're negative. Finally, situation means that the force is pointing to the order direction which in this case, it's the left and finally, on the last item. We have an acceleration off zero meters per second square and these given the force back to that his secrets to three times zero minus nine. Which night? Minus nine. New toes. Therefore on the third item two. You mind new terms to do that? Just finish this here in the first item. True. You're six. New comes two. You're right.

Brazilian Center for Research in Physics