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Course: Mechanics (Essentials) - Class 11th>Unit 6

Lesson 7: When is a lift cable most likely to break - while going up or down?

Mild and medium tension

David explains how to solve tension problems for hanging objects. Created by David SantoPietro.

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• What if the angle is not given?
How do we calculate it?
Using the given tensions.
• What's not shown on the video is the fact that if you draw all of the force vectors to scale and place them end-on-end they form a closed polygon (if there is no acceleration), where there are 3 forces this is a triangle. In the case shown, an object with mass being suspended by 2 strings at different angles (tension forces given but not angles), you can draw a triangle with each of the sides a scaled length of the tension in the respective strings.

You can calculate the angles in a triangle with 3 known side lengths using the 'cosine rule' c² = a² + b² - 2ab.cos(C). Solve for C. This will give the angles the forces MUST act at, thereby giving the angles of the strings.
• In the apple problem when you add 5N and we solve for T, why is gravity a positive number? Why do you not use -9.8? (time )
• Good question. You have to be very careful with negative signs when you translate your force diagrams into equations. Anytime you write the acceleration due to gravity as "g", you should always say that "g = 9.8 m/s^2", that is, "g" is the magnitude of the acceleration due to gravity and is always positive. Then, in order to correctly have gravity pull downward, as you can see the arrow labelled "mg" in the diagram points down, it becomes a force of `-mg` when you write the equation. In his equation, &Sigma; F becomes T - mg. T is positive because it points up, mg is subtracted because it points down. So that is where the minus sign comes in. If you put in another minus sign, it would switch back to positive and your equation would be incorrect.
• Why doesn't David just use the Pythagorean Theorem here?
• He could. There are usually more than a couple ways to solve a problem. As you can see using Pythagoras sqrt(60^2 - 30^2) = 30*sqrt(3) as in the video. However it makes sense that he used trig because it's good to be consistent when making calculations; T1 could only be found using trig.
• Why are T2 and T1x equal if they are pulling in opposite directions? Does this calculations tell you only the magnitude but not the direction?
• "Does this calculations tell you only the magnitude but not the direction?"
Yes. The magnitudes of T_2 and T_1x are equal.
• Sorry if this is a stupid question.Can't tension be present in any long structures,other than ropes?Like maybe if i make an iron rod and use it to pull a car?]
Also,at can't the box pull the wall?

Thanks.
• Yes, tension can be present in an iron rod, for example. Though an iron rod will tend to have a significant amount of mass, so pretending it's massless might be a little less accurate.

The box could theoretically pull down the wall, yes, if the wall was really poorly built. We're assuming that the wall and ceiling are stable.
• If T1y is 30 and T1 is 60 why T1x isn't equal 30?
• Because T1y and T1x are the magnitudes of vectors. The x and y components add up to the total T1, but they add as vectors, not like numbers. The x and y components are the legs of a right triangle with a hypotenuse equal to T1, so you would use the Pythagorean theorem,
(T1x)^2 + (T1y)^2 = T1^2
• Why is the gravity positive in this video? When is the time it should be used as a negative?
• Gravity can be negative or positive, it just depends on how you choose to define your directions. If you decide up is positive, then gravity is negative. If you decide down is positive, gravity is positive. Gravity doesn't know about negative or positive. It just points down.
• Forgive me, I haven't taken a math or science class in over a decade. When solving for T1y at , we add 30N to both sides. Why do they not cancel each other out?
(1 vote)
• they cancel each other but when added to 0 it doesn't get canceled . so, there is another 30 N left in the L.H.S.
• If T1 perpendicular the roof, then T1 = T1y = mg = 30N. T1x = 0, but T2 dont equal 0.
T2 = mg * sin(45) or T2 = mg * cos(45), because angle of movement the board = 45 grade ?
(1 vote)
• The first thing you need to understand is that when applying Newton's Second law, i.e. `F_net = ma`, you choose a coordinate system axis, usually XY-axis to find the components of the forces acting along each axis and then apply F = ma to each axis separately.
Now if T1 is perpendicular then there are two forces along the Y axis. T1 up and weight, mg down. So your Second law equation along Y axis becomes: T1 - mg = ma_y
Now along X axis, there's only one force T2 acting, so you'd write: T2 = ma_x
Which means, the block will not remain in equilibrium, because the forces are not balanced. It would accelerate in the direction in which T2 acts as soon as you let go of it.