Finding minimum values for problems

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To determine the shortest sling ABC for lifting a 1000N block with a maximum tension of 1300N, the tension in the sling can be expressed as T sin(theta) = W/2, where theta is the angle at which the sling meets the block. Calculating the angle corresponding to the maximum tension is essential for further calculations. Once the angle is known, the length of the chain can be derived using trigonometric relationships in the formed triangle. Understanding these relationships allows for the determination of the minimum length of the sling required. The discussion emphasizes the importance of deriving the angle before calculating the sling length.
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Homework Statement


Hi guys, really stuck on this one.

A 1000N black is to be lifted using a chain sling (as shown). If the tension in the chain sling is not to exceed 1300N, find the shortest sling ABC that can be used.
A is the most left point, B is the most right point and C is the top point.




Homework Equations





The Attempt at a Solution



I think i have to take the derivative of something to find the minimum but have no idea how to go about that.

Picture_2.jpg

 
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You shouldn't need to use calculus on this one. Since you've been given the maximal value of the tension, start by writing an expression that gives the tension in the sling as a function of the angle where the sling meets the block. What is the value of the angle that corresponds to the given maximal tension?
 
I think I've got it.

With this formula
T sin(theta) = W/2
i can get the angle cause i know the max tension, but then how do i get the length of the chain from that?
 
tooperoo said:
I think I've got it.

With this formula
T sin(theta) = W/2
i can get the angle cause i know the max tension, but then how do i get the length of the chain from that?
If you know the angle and at least one triangle side length...
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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