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Aristotle
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Homework Statement
Homework Equations
Static equilibrium: Net force & net torque = 0
SteamKing said:You are introducing an extra quantity d1 into your calculations, which will be difficult to calculate. Find an expression for sin θ based on L and H for the gantry crane as shown in the diagram.
Aristotle said:Either way even with replacing d1 with H, I still get Ft = (mgx+MgL/2) /(L sin(theta) ) . Am I on the right step?
SteamKing said:d1 ≠ H, and the expression for sin θ is a little more complicated than that. Your expression for FT is correct.
Jilang said:Yes, it's absolutely fine. But can you express sin theta in terms of H and L ?
Aristotle said:If I can't call the line of the pivot point perpendicular to the cable d1, what should I call it? I'm a little confused on what you mean. Isn't that all I'm looking for anyways: the tension in the cable as a function of the load position x? - which was the expression i found?. :/
SteamKing said:There's another triangle (which you are overlooking) which can give you an expression for sin θ. (Hint: the cable holding the support arm forms the hypotenuse of this triangle)
Aristotle said:The only triangle I see is the top triangle and bottom triangle and the triangle on the left with d1.
sin theta = H/L
How else can you derive the sin theta?
Sorry about that, sin theta = H / sqrt (L^2 + H^2) :DSteamKing said:sin θ is not H / L. You should review your trigonometry, especially the definitions of the sine, the cosine, and the tangent.
Torque is a measure of how much a force acting on an object causes that object to rotate. It is calculated by multiplying the force applied by the distance from the pivot point to the point where the force is applied.
Although torque and force are related, they are not the same thing. Force is a push or pull on an object, while torque is the measure of how that force causes an object to rotate. In other words, torque is a force that causes rotation.
In order for an object to be in static equilibrium, the sum of all the forces acting on the object must be zero and the sum of all the torques acting on the object must also be zero. This means that the forces and torques acting on the object are balanced, and the object is not moving or rotating.
Torque can be increased by either increasing the force applied or by increasing the distance from the pivot point where the force is applied. This is why longer wrenches are more effective at loosening tight bolts, as they allow for a greater distance from the pivot point and therefore a greater torque.
The two main factors that affect torque are the force applied and the distance from the pivot point. Other factors that can affect torque include the angle at which the force is applied, the direction of the force, and the properties of the object itself (such as its shape or mass distribution).