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The winch takes in cable at a constant rate of 130 mm/s. If the cylinder mass is 115 kg, determine the tension in cable 1. Neglect all friction.

Answer :

The tension in the cable raising a mass of 120.0 kg with an acceleration of 1.3 m/s² is calculated using Newton's second law, resulting in 156 Newtons.

To determine the tension in the cable that raises a mass of 120.0 kg with an acceleration of 1.3 m/s², we need to apply 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 (F = ma). In this scenario, the only forces acting on the mass are gravity and the tension in the cable.

First, calculate the gravitational force (weight) acting on the mass:
Weight (Fg) = mass (m) imes acceleration due to gravity (g)
Fg = 120 kg×9.8 m/s² = 1176 N.

Since the object is accelerating upward, we need to account for this additional force required. The total force (Ft) needed to raise the mass with the given acceleration is:
Ft = mass (m) × total acceleration (g + a)
Ft = 120 kg ×(9.8 + 1.3) m/s² = 120 kg × 11.1 m/s² = 1332 N.

The tension in the cable is equal to the total force needed minus the weight of the object, which gives us the net force required to achieve the acceleration:
Tension (T) = Ft - Fg
T = 1332 N - 1176 N = 156 N.

Therefore, the tension in the cable is 156 Newtons.

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