Mechanics- connected particles

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Discussion Overview

The discussion revolves around a mechanics problem involving two connected particles, A and B, attached to a string over a pulley. The scenario includes calculating the maximum height reached by particle B when particle A hits the ground and determining the total time until B hits the ground after the string is cut. The focus is on the application of kinematic equations and the forces acting on the particles.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Some participants express confusion about how to calculate the maximum height reached by particle B and the total time until it hits the ground.
  • One participant claims to understand the calculations but does not provide details on their reasoning.
  • Another participant shares their calculations for the time taken for particle A to hit the ground and the maximum height reached by particle B, but expresses difficulty in calculating the time after the string is cut.
  • A participant mentions the equations of motion and the forces acting on the particles, suggesting a method to solve for acceleration and subsequent heights and times.

Areas of Agreement / Disagreement

Participants generally express confusion and uncertainty regarding the calculations involved in the problem. There is no consensus on the correct approach or final answers, as multiple participants are struggling with different aspects of the problem.

Contextual Notes

Participants reference various equations of motion and forces but do not clarify assumptions or provide complete solutions. The discussion lacks resolution on the specific calculations needed to arrive at the answers.

Shah 72
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Two particles A and B are attached to the ends of a light inextensible string, which passes over a smooth pulley. Particle A has mass 8 kg and particle B has mass 5kg. Both the particles are held 1.2m above the ground. The system is released from rest and the particles move vertically.
a) when particle A hits the ground, it does not bounce. Find the max height reached by particle B
b) when particle A hits the ground, the string is cut. Find the total time from being released from rest until B hits the ground.
I don't understand how to calculate.
 
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Shah 72 said:
Two particles A and B are attached to the ends of a light inextensible string, which passes over a smooth pulley. Particle A has mass 8 kg and particle B has mass 5kg. Both the particles are held 1.2m above the ground. The system is released from rest and the particles move vertically.
a) when particle A hits the ground, it does not bounce. Find the max height reached by particle B
b) when particle A hits the ground, the string is cut. Find the total time from being released from rest until B hits the ground.
I don't understand how to calculate.
I understood how to calculate. Thanks!
 
Shah 72 said:
Two particles A and B are attached to the ends of a light inextensible string, which passes over a smooth pulley. Particle A has mass 8 kg and particle B has mass 5kg. Both the particles are held 1.2m above the ground. The system is released from rest and the particles move vertically.
a) when particle A hits the ground, it does not bounce. Find the max height reached by particle B
b) when particle A hits the ground, the string is cut. Find the total time from being released from rest until B hits the ground.
Iam not getting the ans for (b)
For the time when A hits the ground
V= u+at
t1= 1.02s
Max height traveled by B is 2.68.
When the string is cut, T= 0, a=-g=-10m/s^2
Iam not able to calculate.
 
how 😭😭
 
Shah 72 said:
Two particles A and B are attached to the ends of a light inextensible string, which passes over a smooth pulley. Particle A has mass 8 kg and particle B has mass 5kg. Both the particles are held 1.2m above the ground. The system is released from rest and the particles move vertically.
a) when particle A hits the ground, it does not bounce. Find the max height reached by particle B
b) when particle A hits the ground, the string is cut. Find the total time from being released from rest until B hits the ground.

maha said:
how 😭😭

$M$ = 8kg, $m$ = 5kg, $T$ is the tension force in the string

$Mg - T = Ma$
$T - mg = ma$

Solve the system of equations for $a$, the magnitude of the acceleration for both masses. Once you find that acceleration, you can find the upward velocity of the smaller mass when the larger one hits the ground …
$v_f^2 = v_0^2 + 2a \Delta y$
At that time, the smaller mass is strictly under the influence of gravity, and one can determine the height the small mass rises above its initial height of 2.4 m, using a variation of the above equation …
$v_f^2 = v_0^2 - 2g \Delta y$

See what you can do from here.
 

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