Mass attached to a rope (simple)

[saltyload]

1. A 1000kg mass is lowered by a rope. If the mass is initially moving at 10m/s, and is decelerating at 1m/s², what is the initial tension T in the rope?



2. T = mg



3. So I tried setting up T = mg, and then since it is decelerating the tension must be less than what it would be if it was in static equilibrium. Then I added ma to side T.

ma + T = mg

Ended up getting T = 9000N, but the answer is 11,000N.

What did I do wrong? I thought my thinking was correct. I thought about a mass in an elevator which would weigh less if elevator moved downward and weigh more if elevator moved up.

 

[Doc Al]

I thought about a mass in an elevator which would weigh less if elevator moved downward and weigh more if elevator moved up.

If the elevator accelerates downward, the mass would 'weigh' less. Acceleration, not movement, is the key.

So what's the direction of the acceleration of the 1000 kg mass? (Read carefully.)

 

[saltyload]

If the elevator accelerates downward, the mass would 'weigh' less. Acceleration, not movement, is the key.

So what's the direction of the acceleration of the 1000 kg mass? (Read carefully.)

AH! the mass is moving downward, but since its decelerating, its accelerating upwards, which increases the tension of the rope!

 

[Doc Al]

Exactly!

 

[rwisz]

Your thinking was correct, but there may have been a mistake in your calculations. When solving for tension in a system, it is important to consider all forces acting on the object. In this case, the mass is being lowered at a constant velocity, so there are two forces acting on it: the force of gravity (mg) and the force of the rope (T). Since the mass is moving at a constant velocity, the net force must be zero. This means that T = mg, which is what you initially set up.

However, when the mass is decelerating, there is an additional force acting on it: the force of acceleration (ma). This force must be added to the equation, so the correct setup is T - ma = mg. Solving for T, we get T = mg + ma = (1000kg)(9.8m/s^2) + (1000kg)(1m/s^2) = 10,800N. This is closer to the given answer of 11,000N.

It is important to carefully analyze all forces acting on an object in order to accurately solve for tension. In this case, the force of acceleration was overlooked, leading to a slightly incorrect answer. Keep in mind that in real world scenarios, there may be other forces acting on the object as well, so it is important to consider all factors when solving for tension.