An object with weigh 20 N hangs from ceiling on end ofwire. Additional force of

Question

An object with weigh 20 N hangs from ceiling on end ofwire. Additional force of 20 N is applied to object throughrope. Find tension in wire attached to ceiling if force isapplied vertically downwards Find tension in wire attached to ceiling and its angle withrespect to vertical if force is applied with rope at angle of 45degrees from horizonal An object with weigh 20 N hangs from ceiling on end ofwire. Additional force of 20 N is applied to object throughrope. Find tension in wire attached to ceiling if force isapplied vertically downwards Find tension in wire attached to ceiling and its angle withrespect to vertical if force is applied with rope at angle of 45degrees from horizonal

Explanation / Answer

The object is in equilibrium in both cases So the tention inthe rope will be the same as the amount of force that ispulling on it. For the first one the object weighs 20 N andyou are adding 20 N more on top of that. that makes thetention in the rope equal to 20 + 20 = 40 N. This is becausethe force is placed vertically downward. Now if you take thatsame force and apply it at a 45 degree angle the tension and thewire will move which is the angle with respect to thevertical. First of all the force componants are found bythese two equations x componant= total force * cos y componant= total force * sin So the two componants are x=20* cos 45=14.14 N y= 20 * sin 45=14.14 N That makes the total downward force be the weight plus the ycomponant. 20+14.14=34.14 N. Adding in the weight changes the angle. First of all tofind the tention you need to find the magnitude of the twocomponants. x^2+y^2=magnitude ^2 34.14^2+14.14^2=36.95 N total force. Now the direction can be found by dividing the y componant bythe x componant and taking the arctan of that to get the newangle. arctan 34.14/14.14=67.5 degrees. Now that is not your answer because the question asks for theangle from the vertical and this equation gave you the angle fromthe horizontal so subtract that from 90 to get the angle from thevertical. 90-67.5=22.5 degrees which is your answer. y componant= total force * sin So the two componants are x=20* cos 45=14.14 N y= 20 * sin 45=14.14 N That makes the total downward force be the weight plus the ycomponant. 20+14.14=34.14 N. Adding in the weight changes the angle. First of all tofind the tention you need to find the magnitude of the twocomponants. x^2+y^2=magnitude ^2 34.14^2+14.14^2=36.95 N total force. Now the direction can be found by dividing the y componant bythe x componant and taking the arctan of that to get the newangle. arctan 34.14/14.14=67.5 degrees. Now that is not your answer because the question asks for theangle from the vertical and this equation gave you the angle fromthe horizontal so subtract that from 90 to get the angle from thevertical. 90-67.5=22.5 degrees which is your answer.

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