MHB Mechanics- connected particles

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SUMMARY

The discussion centers on the mechanics of two connected particles, A and B, with masses of 8 kg and 5 kg respectively, attached to a light inextensible string over a smooth pulley. When released from a height of 1.2 m, particle A falls and does not bounce upon hitting the ground, allowing particle B to rise to a maximum height of 2.68 m. The total time from release until particle B hits the ground after the string is cut is calculated to be 1.02 seconds, considering the acceleration due to gravity.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with kinematic equations
  • Basic knowledge of gravitational acceleration (g = 10 m/s²)
  • Concept of tension in a string system
NEXT STEPS
  • Study the derivation of kinematic equations for vertical motion
  • Learn about tension force calculations in connected mass systems
  • Explore energy conservation principles in mechanics
  • Investigate the effects of cutting tension in pulley systems
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Students studying physics, particularly those focusing on mechanics, as well as educators and tutors looking for practical examples of connected particle systems and their dynamics.

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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