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Problem 9 Easy Difficulty

ssm Two forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ are applied to an object whose mass is 8.0 $\mathrm{kg}$ . The larger force is $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ . When both forces point due east, the object's acceleration has a magnitude of 0.50 $\mathrm{m} / \mathrm{s}^{2}$ . However, when $\overline{\mathrm{F}}_{\mathrm{A}}$ points due east and $\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ points due west, the acceleration is 0.40 $\mathrm{m} / \mathrm{s}^{2}$ due east. Find (a) the magnitude of $\overrightarrow{\mathbf{F}}_{\mathbf{A}}$ and $\quad(\mathbf{b})$ the magnitude of $\overrightarrow{\mathbf{F}}_{\mathbf{B}}$.

Answer

3.6 $\mathrm{N}$
0.40 $\mathrm{N}$

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Video Transcript

the question. We can apply Newton's second law in both situations, So forget your situation. Newton's second law tells us that that force is it close to the object's mass times acceleration. But the objects net force in this case is close to a clothes. Be knows that I'm inducting that everyone pointing towards the right. It's positive, and everyone pointing toward the left is negative. So here we have f a bus at me when these is a question of mass times acceleration on the second situation in that force, let me. What is the second situation? The net force is equals again to the mass times declaration. But now exploration is different. So let's call it a crime and the net force is given by eight miners. FB Because now the force be is pointing to the left. And he was close to the mass times the new exploration. So this is what to get by using new tone. Second walk. Now what can we do? You too. So for F A A and F B well, note that it is a system of equations. In the first situation, we have a what be you close to eight times zero like haIf because for therefore, in the first situation, we have a key. Be he's sick. What's true for In the second situation, we have a minus. B equals two zero 0.4 times eight, which is equals True three 12 Therefore, our system of equation is the following has eight plus f b is equal to four on the same time f a minor that me in the post entry points. True, then how can the company the Force f K for instance? Well, for ft, we only have two. Some both equations. We can see these because here we have plus FDA and plus FDA again, which gives us true kinds as a now for f me, we have plus F B minus f b and this zero there is an exact cancellation. Then two times a day is close to four plus 7.2, which is equally true. Seven. It's true now the Force ft People's too 7.2 divided by True, which is a ghost to tree 0.6 for a is 3.6 new terms. Now how can it cos the force at me? Well, now that we know the Force eight. We can play getting either these equations or this equation to calculate its beak. Major choice. It should not make any difference. I would choose the 1st 1 Two 3.6 plus B is equal to four. Then me music was before minus 3.6. Then they forced me is equal to 0.4 new terms. It's very easy to check this. 3.6 plus 0.4 is in fact, equals before. At the same time, 3.6 minor 0.4 is the question 3.2.