Answer :
Final answer:
To calculate the tension in a rope for a climbing gymnast, use Newton's second law of motion. The tension in the rope is equal to the weight of the gymnast when climbing at a constant speed. When the gymnast accelerates upward, the tension is the sum of the weight and the force due to acceleration.
Explanation:
To calculate the tension in a rope, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. For part (a) where the gymnast climbs at a constant speed, the net force is zero, so the tension in the rope is equal to the weight of the gymnast. Tension = Weight = mass × acceleration due to gravity = 72.5 kg × 9.8 m/s² = 710.5 N.
For part (b) where the gymnast accelerates upward at a rate of 1.50 m/s², we need to consider the additional force required to accelerate the gymnast. The net force is given by the equation F = m × (g + a), where F is the net force, m is the mass, g is the acceleration due to gravity, and a is the upward acceleration. Tension = Weight + Force due to acceleration = (mass × acceleration due to gravity) + (mass × upward acceleration) = 72.5 kg × 9.8 m/s² + 72.5 kg × 1.50 m/s² = 817.25 N.
