Final answer:
The tension in the rope is 490 N when the box moves up at a steady speed. When the box is moving up but slowing down at 5.0 m/s², the tension is reduced to 240 N, because the tension has to counteract both the gravity and the deceleration.
Step-by-step explanation:
When a box hangs from a rope and moves at a constant velocity, the tension in the rope is equal to the weight of the box. The weight can be calculated with the formula T = mg, where 'm' represents the mass of the box and 'g' is the acceleration due to gravity (9.8 m/s²). In this case, the tension for a 50 kg box is T = 50 kg × 9.8 m/s² = 490 N.
If the box is moving upwards with a velocity (Vy) of 5.0 m/s and slowing down at a rate of 5.0 m/s², the tension is given by T = m(g - a), where 'a' is the deceleration. Using the given values: T = 50 kg × (9.8 - 5.0) m/s² = 50 kg × 4.8 m/s² = 240 N.
The tension decreases because the upward force (tension) is now also providing the force required to decelerate the box.