Question

A monkey of mass 40kg climbs on a rope as shown in figure which can bear a maximum tension of 600N. In which of the following cases will the rope break: The monkey

 

(a) climbs up with an acceleration of 6ms^-2 

(b) climbs down with an acceleration of 4ms^-2 

(c) climbs up with a uniform speed of 5ms^-1 

(d) falls down the rope nearly freely under gravity? 

(Ignore the mass of the rope)

Answer 1

Given Mass of monkey = 40 kg, acceleration due to gravity = 10 m/s², rope tension = 600 N 

case (a) 

= T- mg = ma   T = m(g + a) = 40 (10+6) =640 N > 600 N so rope will break. 

case (b)

 T = m(g- a) = 40 (10- 4) =240 N < 600 N so rope will not break. 

case (c)

 T- mg = 0, T = mg = 40 *10 =400 N < 600 N so rope will not break.

Case (d) 

When the monkey falls freely under gravity, acceleration will become equal to the acceleration due to gravity, i.e., a = g 

Using Newton’s second law of motion, we can write the equation of motion as: 

mg – T = mg

 ∴ T = m(g – g) = 0 

Since T < T_max , the rope will not break in this case.

Answer 2

(a) T - 400 = 240, T = 640N,

(b) 400 - T = 160, T = 240N

(c) T = 400N

(d) T = 0