Finding FE, Tension & Acceleration in a 3-Block Frictionless Ramp Setup

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SUMMARY

This discussion focuses on calculating the force 'FE' and the tensions in a three-block system on a frictionless 45° ramp. The top block (m1=1.00 kg) experiences a force that holds all blocks in place, while the middle block (m2=2.00 kg) and bottom block (m3=3.00 kg) contribute to the tension in the ropes. When FE is removed, the blocks slide down the ramp, requiring calculations for their acceleration and the new tensions in the ropes. Additionally, when the force is doubled to 2FE, further analysis of acceleration and tensions is necessary.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Basic knowledge of forces and tension in ropes
  • Familiarity with inclined plane physics
  • Ability to perform calculations involving mass and acceleration
NEXT STEPS
  • Calculate the gravitational force acting on each block on the incline
  • Learn about tension force equations in multi-block systems
  • Explore dynamics of frictionless inclined planes
  • Study the effects of varying forces on block acceleration
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Physics students, educators, and anyone interested in understanding dynamics and forces in multi-body systems on inclined planes.

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three blocks on a frictionless 45° ramp held together by massless ropes
top block's mass, m1=1.00 kg.
middle block's mass, m2=2.00 kg
bottom block's mass, m3=3.00 kg.
1. the force 'FE' is exerted on block one and is just enough to hold all the blocks in place
find FE and the tensions of the ropes
2. FE is no longer acting on the blocks so they slide down the ramp, find the acceleration of the blocks and the tensions in the ropes
3. 2FE is now acting on block one, find acceleration of blocks and tensions in the ropes


All I really need help with is the tension
 
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Basically it's the force coming from the rope

So for example, the top block is sitting still for part 1 and has what amounts to 5kg of mass hanging on that segment of rope. Figure out the force of gravity going down the incline caused by the 5kg, that force will be the tension in the rope, it's how much force the rope has to apply to hold them there

The tension in the other segment(connecting blocks 2 and 3), well that segment of rope is only supporting the 3 kg mass
 

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