Mechanics- connected particles

In summary, the conversation discussed the calculation of friction, tension, and acceleration in a system involving a rope and a mass. The correct value for tension was found to be 84N, which was different from the textbook answer. The time was also calculated to be 1 second. The equations used were Mg-T=Ma and T-mg(sinθ+μcosθ)=ma, and the final values for acceleration and tension were 3m/s^2 and 84N, respectively.
  • #1
Shah 72
MHB
274
0
20210530_210957.jpg

Friction= 1/(sqroot12)×80 cos 30= 20N
I get two equations
T-20=8a and 120-T=12a
a=5m/s^2
I don't know how to calculate the time. Also with this value of acceleration tension value is wrong and the textbook ans is 84N
 
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  • #2
Shah 72 said:
View attachment 11166
Friction= 1/(sqroot12)×80 cos 30= 20N
I get two equations
T-20=8a and 120-T=12a
a=5m/s^2
I don't know how to calculate the time. Also with this value of acceleration tension value is wrong and the textbook ans is 84N
I calculated the time
S=ut +1/2at^2
(2+1.5)= 1/2×5×t^2
I got t=1s
For q(b) iam getting the ans tension in the rope= 60N but the textbook ans is 84N. Pls help
 
  • #3
$Mg - T = Ma$
$T - mg(\sin{\theta} + \mu \cos{\theta}) = ma$
———————————————————————
$Mg - mg(\sin{\theta} + \mu \cos{\theta}) = a(M+m)$

$a = \dfrac{g[M-m(\sin{\theta}+ \mu \cos{\theta})]}{M+m} = \dfrac{10\left[12-8\left(\frac{3}{4}\right) \right]}{20}= 3 \, m/s^2$

$T = M(g-a) = 12(7) = 84$N
 
  • #4
skeeter said:
$Mg - T = Ma$
$T - mg(\sin{\theta} + \mu \cos{\theta}) = ma$
———————————————————————
$Mg - mg(\sin{\theta} + \mu \cos{\theta}) = a(M+m)$

$a = \dfrac{g[M-m(\sin{\theta}+ \mu \cos{\theta})]}{M+m} = \dfrac{10\left[12-8\left(\frac{3}{4}\right) \right]}{20}= 3 \, m/s^2$

$T = M(g-a) = 12(7) = 84$N
Thank you very much!
 

FAQ: Mechanics- connected particles

What is the definition of "mechanics-connected particles"?

Mechanics-connected particles refer to a system of two or more particles that are connected by some type of physical interaction, such as a spring or rope.

What are the key principles of mechanics-connected particles?

The key principles of mechanics-connected particles include Newton's laws of motion, conservation of energy, and conservation of momentum.

How do you analyze the motion of mechanics-connected particles?

To analyze the motion of mechanics-connected particles, you can use equations of motion, free body diagrams, and energy conservation equations.

What are some real-world applications of mechanics-connected particles?

Mechanics-connected particles have numerous real-world applications, such as in engineering and construction, where understanding the behavior of connected structures is crucial for safety and stability.

What are some common challenges when studying mechanics-connected particles?

Some common challenges when studying mechanics-connected particles include accounting for friction, dealing with complex systems, and accurately measuring and analyzing data.

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