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Problem 57 Hard Difficulty

ssm A worker stands still on a roof sloped at an angle of $36^{\circ}$ above the horizontal. He is prevented from slipping by a static frictional force of 390 N. Find the mass of the worker.

Answer

68 $\mathrm{kg}$

Discussion

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EF

Ehleketani F.

April 5, 2021

Vector A has magnitude 4 units, vector B has magnitude 6 unit's. The angle between A and B is 60. Calculate the magnitude of 2A +3B

EF

Ehleketani F.

April 5, 2021

Vector A has magnitude 4 units, vector B has magnitude 6 unit's. The angle between A and B is 60. Calculate the magnitude of 2A +3B

Video Transcript

to solve this question. It's a good call to use the following your reference frame in order to apply Newton's second law. So a very good reference frame for this question is the following. This will be my why direction and this will be my ex direction. Then, using this reference frame, we will apply new tone Second Law on both faxes, the white and the Axe one. Then we get the following by applying Newton's second law to the Y axis, we get that the net force on the Y direction Is it close to the mass off the worker times Its acceleration in the Y direction notes that the worker isn't falling inside the house and nor flying your way. Therefore, it's a standing still in the Y direction, so the acceleration in that direction is equal to zero. Then the net force in the Y direction is equal to zero. But the net force on the wider connection has two components. The normal force which points to the positive direction according to our reference frame normal and a portion off. The weight force is also pointing in this direction. Which portion he's one. The weight force can be. They compose it as two forces one point in the direction which I will call the y component off the weight force and another one pointing in the direction which I will call the acts component off the weight force. Then for the white direction. New turn, second law, we get the normal force. Minors. The Y component off the weight force is equal to zero. Then the normal force is equals to the Y component off the weight force. Now we apply Newton's second law off on the order direction on the X direction. This tells us that the net force the X direction is equals to the mass off the worker times acceleration. Now the worker isn't clinging for their The roof more is leaping down the roof. It's a standing still in this direction. True, then acceleration Dax direction is it close to zero? So the net force in the X direction is equals to zero. But the net force in the X direction has two components to one of them is the frictional force, which is pointing to the positive direction off the X direction. So frictional force and the other component he's the X component off the weight force, which is pointing to the negative direction off the X axis, then minus the weight component X, and this is equal to zero. Therefore, the fictional force easy close to the weight forest component acts. But we know that the fictional force is equals to 390 new terms. Therefore, the X component off the weight force. Easy close to 390. Then we have to discover. Now why is the weight off the worker? How can we do that? We can do that by looking at the components off. The weight force we have erecting will try and deal with the weight which looks like this I bought The news is the full weight force. These side of triangle is the Y component. On this side of the triangle is the X component. And we have a 90 degree angle here and the 36 degree angle here. Why is these angle equals to 36 degree? Well, just take a look at the figure. This angle is 36 degrees at the same time. There is a right on go right here. Then this triangle is a rectangle triangle the reform. If this is the 90 degrees angle, these orders angle here will be 90 my nose 36 degrees, which is equals to 54 degrees. Then look at the following this angle between the roof and the Y component off the weight force is an angle off 90 degrees. Okay, then what is this? A new If we know that he's one easy goes to 54. Well, this full angle has 90 degrees, then this angle has 90 minus 54 degrees, which is again 36 degrees. So this is why this angle is because the tortoise six degrees now to calculate the X component, we can use the sign off 36 degrees because the sign off 30 16 race is eco's, too the opposite side of the triangle, which is the weight component acts divided by the high party news, which is the weight force itself. Then the weak force component X is equal to the weight forced times. The sign off 36 degrees. No, we use these equations years to get the following 390 he's equals True, the weight forced times The sign off 36 degrees. Then no wait. Forced is equals to 390 divided by this sign off 36 degrees. Then finally, this gives us a weight force off approximately 663.5 new Thomas. Then to find the mass off the worker, we have to remember that the weight force is given by the mass off the object times acceleration of gravity. The acceleration of gravity near the surface of the earth is approximately 9.8 meters per second squared, then 663.5 new terms, which is the magnitude off. The weight force is equal to the mass off the worker times 9.8, then the mass off the worker is a close to 663.5, divided by 9.8, which is approximately 68 kilograms. Note that there wa sno usage for these older equation from you don't second law. There is no problem with that

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