Rope and Bird Mechanics: Calculating the Force on a Hanging Rope

[vipulgoyal]

Why anyone is not answering this question...

Homework Statement

a uniform rope of mass m hangs freely from the ceiling. A bird of mass M climbs up the rope with an acceleration A. the force exerted by the rope on the ceiling is

Homework Equations

T = mg + M(g+a) is answer

The Attempt at a Solution

shouldnt we consider M of the rope as a variable here depending upon the position of bird on the rope??

 

[tiny-tim]

hivipulgoyal!

shouldnt we consider M of the rope as a variable here depending upon the position of bird on the rope??

no …

the forces on the bird from the rope must be M(g + a), so that M(g + a) + (-Mg) = Ma

and then the forces on the rope are -mg, -M(g + a) from the bird, and the force from the ceiling

 

[vipulgoyal]

hivipulgoyal!


no …

the forces on the bird from the rope must be M(g + a), so that M(g + a) + (-Mg) = Ma

and then the forces on the rope are -mg, -M(g + a) from the bird, and the force from the ceiling

why are we considering the force exerted by the rope on the bird i mean the force M(g+a) is due to gravity and acceleration of the bird

 

[tiny-tim]

… the force M(g+a) is due to gravity and acceleration of the bird

sorry, but this is nonsense …

the force M(g+a) is the force exerted by the rope on the bird …

it is the force needed to produce a net force of Ma​

 

[vipulgoyal]

""the force M(g+a) is the force exerted by the rope on the bird …"""
SORRY BUT THIS IS THE FORCE DUE TO GRAVITY as acc. to you if i jus delete the rope from the equation then there will be no force on the bird and it will be weightless..! does it makes sense...?? not to me at least

 

[tiny-tim]

""the force M(g+a) is the force exerted by the rope on the bird …"""
SORRY BUT THIS IS THE FORCE DUE TO GRAVITY as acc. to you if i jus delete the rope from the equation then there will be no force on the bird and it will be weightless..! does it makes sense...?? not to me at least

draw a free body diagram for the forces on the bird …

there are exactly two forces, the weight (-Mg) and the reaction force from the rope (R) …

the total force is R - Mg, and this must equal ma …

R - Mg = Ma

or R = M(g + a) ​

 

[vipulgoyal]

T = mg + M(g+a) is answer

 

[tiny-tim]

T = mg + M(g+a) is answer

yes, that's for the force on the rope from the ceiling …

to find that, you need a free body diagram for the forces on the rope …

there are three forces on the rope …

what are they, and how do they add up? ​