5.33 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)

<p>Mass of the monkey = 40 kg</p><p>Maximum tension of the rope Tmax = 600 N</p><p><strong> (a)</strong> When the monkey climbs up with an acceleration of 6m / s²</p><p>Tension in the rope, T – mg = ma</p><p>T = m (g+a) = 40 (10+6)= 640 N</p><p>Since T &gt; Tmax, the rope will break</p><p>&nbsp;</p><p><strong> (b)</strong> When the monkey climbs down with an acceleration of 4m/s²</p><p>Tension in the rope T is given by mg – T = ma</p><p>T = m (g-a) = 40 (10-4) N = 240 N</p><p>Since T &lt; T max, the rope will not break</p><p>&nbsp;</p><p><strong> (c)</strong> Climbs up with an uniform speed of 5 m/s</p><p>In this case, the acceleration = 0</p><p>The tension in the rope is given by</p><p>T –mg = ma</p><p>T = mg = 40&nbsp;<span title="Click to copy mathml"><math><mo>*</mo><mn>10</mn><mo>=</mo><mn>400</mn><mi></mi><mi>N</mi></math></span></p><p>Since T &lt; Tmax, the rope will not break</p><p>&nbsp;</p><p><strong> (d)</strong> When the monkey falls down freely under gravity</p><p>The tension in the rope is given by the equation</p><p>T + mg = ma, since a = g, T = 0</p><p>Since T &lt; Tmax, the rope will not break</p>

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