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A 50kg box hangs from a rope.

What is the tension in the rope if the box moves up at a steady 5.0m/s ?
What is the tension in the rope if the box has Vy= 5.0 and is slowing down at 5.0m/s2 ?

User Ilya Vo
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1 Answer

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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.

User Bilel
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