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Physics Mechanics- connected particles

Shah 72

Member
Apr 14, 2021
187
Two smooth pulleys are 8m apart at the same horizontal level. A light inextensible rope passes over the pulleys and a box of mass 5kg hangs at each end of the rope. A third box of mass m kg is attached to the midpoint of the rope and hangs between the pulleys so that all the three boxes are at the same horizontal16219516208853352424674701945122.jpg level. The total length of the box is 16m. Find the value of m
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935
total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg
 
Last edited:

Shah 72

Member
Apr 14, 2021
187
total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg
Iam so so sorry again typo error. Its the total length of the rope = 16m
 

Shah 72

Member
Apr 14, 2021
187
total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg
The ans in the textbook says 6 kg.
 

Shah 72

Member
Apr 14, 2021
187
total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg
Can you pls pls tell me how to work it out?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935

Shah 72

Member
Apr 14, 2021
187
6 kg is correct … I used the wrong value for a trig ratio.
Can you pls pls tell me the method you worked it out? I have no clue how to solve it.
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935
3D285147-A12D-4FFE-868E-957D07107419.jpeg
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935
$h + \sqrt{h^2+16} = 8$

 

Shah 72

Member
Apr 14, 2021
187

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
935
$h + \sqrt{h^2+16} = 8$

$\sqrt{h^2+16} = 8-h$

square both sides …

$h^2+16 = 64 - 16h + h^2$

$16h = 48$

$h =3$

check solution …

$3 + \sqrt{3^2+16} = 3 + 5 = 8$

checks good.

recommend you review solving radical equations …
 

Shah 72

Member
Apr 14, 2021
187
$h + \sqrt{h^2+16} = 8$

$\sqrt{h^2+16} = 8-h$

square both sides …

$h^2+16 = 64 - 16h + h^2$

$16h = 48$

$h =3$

check solution …

$3 + \sqrt{3^2+16} = 3 + 5 = 8$

checks good.

recommend you review solving radical equations …
Thank you so so much!!! None of these things are explained in the textbook. Iam really struggling with the pulley and string questions. I will surely look into solving radical equations.