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Answer :
Final answer:
To calculate the tension in the cable lifting a man with a weight of 649 N and an upward acceleration of 1.61 m/s², Newton's second law is applied. After determining the man's mass as 66.2 kg, the tension in the cable needed is found to be 746.86 N, which accounts for both the man's weight and the upward acceleration.
Explanation:
The student's question involves determining the tension in the cable of a rescue operation when a man with a weight of 649 N is given an initial upward acceleration of 1.61 m/s². To solve this, we will apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by the acceleration (F=ma).
Firstly, we need to calculate the mass of the man. His weight is given by the force of gravity acting on him, which is the product of his mass (m) and the acceleration due to gravity (g), i.e. Weight = m × g. Given that the acceleration due to gravity is approximately 9.81 m/s², we can find the man's mass:
m = Weight / g = 649 N / 9.81 m/s² ≈ 66.2 kg.
Next, we can calculate the total force needed to both counteract the man's weight and provide the upward acceleration using:
F_net = m × (g + a) = 66.2 kg × (9.81 m/s² + 1.61 m/s²) ≈ 746.86 N.
Therefore, the tension in the cable must be 746.86 N to both lift the man with the given acceleration and overcome the force of gravity.
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