To find the rope's tension, we add the force due to gravity (weight) to the force required for upward acceleration. The weight is 382.2 N, and the force of acceleration is 124.8 N. The total tension in the rope is thus 507.0 N.
Step-by-step explanation:
To calculate the tension in the rope, we need to consider two forces acting on the mass: the force due to gravity (weight) and the force required to accelerate the mass upwards. The tension in the rope must counteract both the weight of the mass and provide the additional force for the acceleration.
First, we calculate the weight of the mass (m) using the force of gravity (g), which is Weight = m × g = 39 kg × 9.8 m/s² = 382.2 N.
Next, we calculate the force required to accelerate the mass upwards (Force of acceleration = m × a), which is Force = 39 kg × 3.2 m/s² = 124.8 N.
The total tension (T) in the rope is the sum of the weight and the force of acceleration, so T = 382.2 N + 124.8 N = 507.0 N.
Therefore, the tension in the rope is 507.0 Newtons, rounded to one decimal place.