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).
Given:
Mass of monkey = 40Kg
Maximum tension that rope can withstand, Tm = 600 N
We need to find the case in which rope will break, i.e. the force should be more than 600 N.
(A) acceleration (Upwards) = 6ms-2
The monkey is moving in upward direction,
From Newton’s 2nd law we can write,
F = ma = T- mg
→ ma = T-mg
→ T = m(a + g)
→ T = 40 Kg( 6 ms-2 + 10 ms-2)
→ T = 640 N
Since T> Tm, the rope is destined for a failure, it will break.
(B) Acceleration (Downwards) = 4 ms-2
The monkey is moving in upward direction,
From Newton’s 2nd law we can write,
F = ma = mg-T
→ ma = mg-T
→ T = m (g - a)
→ T = 40 Kg (10 ms-2 - 4 ms-2)
→ T = 240 N
Since T< Tm, the rope will not break.
(B) Acceleration, a = 0ms-2
Climbing velocity, v = 5ms-1
Using Newton’s 2rd law we can write,
F = ma = T-mg
→ ma = T-mg
→ T = mg
→ T = 40Kg × 10 ms-2
→ T = 400 N
Since T<Tm, the rope will not break.
(C) If the monkey is free falling, i.e. a = g;
Using Newton’s 2nd law of motion, we can write,
F = mg-T = mg
T = mg-mg
T = 0 N
Since, T< Tm, the rope will not break.