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A 67 kg man climbs up the rope with an acceleration of 0.25 m/s\(^2\), measured relative to the rope. (See Figure 1)

Answer :

Final answer:

The tension in the rope when the 67 kg man is climbing it with an acceleration of 0.25 m/s^2 can be determined using Newton's Second Law. When calculated, it gives the tension experienced by the man.

Explanation:

The question is focused on determining the tension in the rope when the 67 kg man is climbing it with an acceleration of 0.25 m/s2. According to Newton's second law, the net force acting on the man includes the net force due to acceleration and his weight, which would oppose his motion upwards. If 'T' denotes the tension in the rope, per Newton's second law, T = m (g + a), where 'm' is the mass of the man, 'g' is the acceleration due to gravity, and 'a' is the acceleration of the man. Thus, substituting the given values, we get T = 67 kg (9.8 m/s2 + 0.25 m/s2), giving us the tension in the rope.

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