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Problem 44 Medium Difficulty

Consult Multiple-Concept Example 9 to explore a model for solving this problem. A person pushes on a 57 -kg refrigerator with a hor-izontal force of $-267 \mathrm{N} ;$ the minus sign indicates that the force points in the $-x$ direction. The coefficient of static friction is $0.65 .$ (a) If the refrigerator does not move, what are the magnitude and direction of the static frictional force that the floor exerts on the refrigerator? (b) What is the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move?

Answer

267 $\mathrm{N}$
360 $\mathrm{N}$

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Video Transcript

for this question, we have to choose as the reference frame. The following everything that is pointing to the left is pointing to the negative direction, and everything that is pointing to the right is pointing to the positive direction. This is because the problem says that the force is minus 267 is minus. Sign indicates a direction off this force, therefore, that they the force must be pointing to the negative direction off our reference frame. So this is like we have to make this choice okay, now perceived to the question. So if the refrigerator does not move, its acceleration is the question zero. Then Newton's second law tells us the following not force easy close to zero, but the net forces compose it off. Two forces the frictional force, which is positive minus the potion force which is 206 decider new terms to the negative interaction. So this is why I put a minus sign there on these is it goes to zero. Therefore, in the situation proposed by the first item, the frictional force is equals to 206 to 7 new terms. Now, for the second item, we have to complete what is the largest possible pushing force that one can apply. So the refrigerator we felt moving it. So the maximum frictional force that can be produced by the static frictional coefficient is given by the following. So the maximum frictional force is it goes to the static frictional coefficient times. The normal force on the normal force is the force that the four is a clerking on the refrigerator, which is this force. Now, how can a couple it normal forest in the situation, You have to note the following in the vertical access. The refrigerator isn't moving so it can't fall below the ground because the ground is holding it there and it also won't start flying out of nowhere. It will just stay on the floor as it is. Therefore, the normal force is equals to the weight force. Then we can use this in this equation to get that the frictional force is equals to the static frictional coefficient times the weight force that acts on the refrigerator and the weight force is given by the mass off the refrigerator times the acceleration of gravity near the surface off the earth. We know that the acceleration of gravity is approximately 9.8 meters per second squared. Therefore, the frictional force is equals to 0.65 times, 57 times 9.8, and this gives us a maximum frictional force off approximately 360 mutants. So this is the maximum pushing force that can be exerted without moving the refrigerator. If we apply a force off 361 new terms, the refrigerator should starts to move.

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