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  • A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey (a) climbs up with an acceleration of 6 m s square inverse (b) climbs down with an acceleration

Q5.33  A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey

(a) climbs up with an acceleration of 6 m s-2
(b) climbs down with an acceleration of 4 m s-2
(c) climbs up with a uniform speed of 5 m s-1
(d) falls down the rope nearly freely under gravity?
    (Ignore the mass of the rope).

    

Answers (1)

best_answer

Given that   Tmax  =  600 N.

(a)   Acceleration of  6 m s-2 in the upward direction:- 

                             Using Newton's law of motion we can write  : 

                                                            T\ -\ mg\ =\ ma

or                                                         T\ =\ 40(6+10)\ =\ 640\ N

      Thus rope will break.

(b)   Acceleration of 4 m s-2 in a downward direction:- 

                                          Using Newton's law of motion we can write  : 

                                                             T\ -\ mg\ =\ ma

or                                                         T\ =\ 40 (10-4)\ =\ 240\ N

       Thus the rope will not break.

 

(c)  Upward with a constant speed of 5 m/s:- 

                              Since speed is constant thus acceleration is 0.

                                         

                                                           T\ -\ mg\ =\ ma

or                                                         T\ =\ 40 (0+10)\ =\ 400\ N

       Thus the rope will not break.

         

(d)  Acceleration is due to gravity (in a downward direction):- 

                             Using Newton's law : 

                                                           T\ -\ mg\ =\ ma

or                                                         T\ =\ 40 (-10+10)\ =\ 0\ N

       Thus the rope will not break.

                                                              

Posted by

Devendra Khairwa

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