MHB Mechanics- connected particles

AI Thread Summary
Two particles, A (8 kg) and B (5 kg), are connected by a string over a pulley and released from a height of 1.2 m. When particle A hits the ground, it does not bounce, and particle B reaches a maximum height of 2.68 m. To find the time until B hits the ground after A's descent, the acceleration of the system can be calculated using the tension equations. The upward velocity of B when A reaches the ground can be determined, followed by calculating the time it takes for B to fall under gravity. The discussion emphasizes the need for proper calculations to solve the problem effectively.
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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