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Thank you We sneak and here's your shmoop du jour

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brought to you by vans which just aren't as groovy

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as they used to be Check the falling image and

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passage Nice hair glasses in your stuff All right What

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is the minimum acceleration that aunt gertrude would have to

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maintain in order for the box to remain attached to

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the van and hear the potential answers all about friction

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Uh no There's A lot going on in this question

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Well let's try to make it simpler on ourselves by

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drawn up the little force diagram right here Okay we've

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got one force the van going in the ex direction

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And this question will label that in for normal force

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to calculate that force we use our trusty formula force

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equals mass times acceleration Then we have to force is

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in the y direction there's gravity pulling down on the

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box and friction pushing it up In order for the

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box to not fall these two forces have to balance

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each other out So the force along the y axis

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is equal to mass times gravity plus friction Well because

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the forces air acting in different directions the first part

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of the equation mass times gravity will be expressed as

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a negative number and here's the equation All right Well

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now let's deal with the friction in our scenario here

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The normal force in is pushing back Against the box

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the normal force and the coefficient of friction together create

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the friction force Here The equation is friction is less

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than or equal to the coefficient of friction times the

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normal force in the equation musa bass represents the coefficient

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of static friction it's important to remember that the question

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is asking us to find the minimum acceleration needed to

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hold the box in place If the normal force is

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too small the friction force won't be strong enough to

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balance out gravity in the box and fall But if

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gertrud floors it jacking the normal force way up a

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friction force will reduce that's because the normal course would

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be pushing on the box so hard that the friction

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force wouldn't have to be doing this much That's why

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the equation has a lesser than or equal to sign

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since we need to find the minimum force needed for

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gertrude to make this crazy scheme work that means that

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friction force needs to be at its highest possible point

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Thor equation for four should really have an equal sign

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okay quick reminder We're trying to balance the forces in

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the uae direction the equation to use is force equals

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the product of negative mass and gravity plus the product

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of the coefficient of friction and the normal force And

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normal force equals mass times acceleration Lastly the result of

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our equation is zero because the forces balance each other

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out right When we simplify the equation and solve for

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acceleration we see that acceleration equals gravity divided by the

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coefficient of friction for ten meters per second squared divided

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by zero point six which comes out to about sixteen

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point seven meters per second squared making option D The

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correct answer And we're thinking of trading in our van 00:03:09.02 --> [endTime] for something easier to parallel park

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