Equivalent Force Calculation for Fixed Quadrant Block with Sliding Rope Tensions

In summary, the conversation discusses the forces applied on a quadrant block, with the block being fixed and allowing the rope to slide freely. T1 and T2 are different due to belt friction, but the system is in static equilibrium. The equivalent force for the whole quad is the vector T1 + T2, which must pass through the intersection of T1 and T2. The conversation also mentions using this force to calculate the reaction force on a welded block. The correctness of the equations for the vertical and horizontal forces is also questioned.
  • #1
kingsgambit
3
0

Homework Statement



http://server7.pictiger.com/img/480530/other/forces.png

http://server7.pictiger.com/img/480530/other/forces.png

I would like to know the forces applied on the quadrant block as shown in the pic. Is there an equivalent force I can take for the whole quad? The block is fixed and allows the rope to slide freely. T1 and T2 (rope tensions) are different due to belt friction, but system is in static equilibrium.


I think there is an equivalent force that acts at the centre of the quad. I need this force to calculate reaction force on welded block. I'm not sure about this though.
 
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  • #2
The "equivalent" force is the vector T1 + T2, and it must pass through the intersection of T1 and T2.
 
  • #3
update needs checking

http://img502.imageshack.us/my.php?image=forcesax4.png

Is the following correct? Please refer to image link.

Vertical : N*cos(A1) + W = R2
Horizontal: N*sin(a1) = R1



T1 and T2 are taken into account by N.
 
  • #4
bumpity bump
 

FAQ: Equivalent Force Calculation for Fixed Quadrant Block with Sliding Rope Tensions

What is the concept of "Rope over slope forces"?

"Rope over slope forces" refers to the forces involved in a rope that is stretched over a slope or incline. These forces include tension, which is the force applied by the rope to keep it taut, and the normal force, which is the force exerted by the slope on the rope perpendicular to its surface.

How do these forces affect the rope?

The tension force in the rope helps to keep it from sagging or losing its shape, while the normal force from the slope can help to support the weight of the rope and any objects hanging from it. These forces can also affect the friction between the rope and the slope, which can impact the stability of the rope.

What factors influence the rope over slope forces?

The main factors that influence rope over slope forces include the angle of the slope, the weight of the rope and any objects attached to it, and the coefficient of friction between the rope and the slope. Other factors such as wind and temperature can also play a role in affecting these forces.

How can we calculate these forces?

To calculate the tension force in the rope, we can use the equation T = mg + ma, where T is the tension force, m is the mass of the rope and any attached objects, g is the acceleration due to gravity, and a is the acceleration of the rope down the slope. The normal force can be calculated using the equation N = mgcosθ, where N is the normal force, m is the mass, g is the acceleration due to gravity, and θ is the angle of the slope.

What are some real-world applications of rope over slope forces?

Rope over slope forces are important in many real-world scenarios, such as rock climbing, zip lining, and skiing. They are also relevant in engineering and construction, as they help determine the stability and safety of structures built on slopes. Understanding these forces is crucial for ensuring the safety and efficiency of any activity or structure involving ropes and slopes.

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