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A 12.0 kg bucket is lowered vertically by a rope in which there is 163N of tension at a given instant. What is the acceleration of the bucket? Is it up or down?
This is what I've done.
f=ma
163N=12.0kg a
163N/ 12.0kg = a
13.6 m/s^2 = a
That should put the bucket going up since it's positive . But it starts saying it's being lowered and I don't really know how the force of gravity fits into it. Any help is appreciated. Thank you
It helps to draw a free-body diagram for problems like this. Your diagram would show the bucket with an upward force of 163 N, and a downward force due to its weight. The resultant force that you have from combining these two forces components is what determines the acceleration of the bucket, using F=ma. If you find a is a positive number, that means the bucket is accelerating upward, but it does not necessarily mean that the velocity is in the up direction - perhaps the bucket is being lowered at a decreasing downard velocity (ie. slowing its rate of descent).
Think about this gravity on earth is 9.8m/s^2
The ONLY way this bucket can accelerate towards the ground faster than 9.8m/s^2 is if it had a net force pushing it down. Since there is tension in the rope we know the net force is in the opposite direction of gravity. THEREFORE, before even attempting this problem, we know the answer must be a fraction of 9.8m/s^2
f=tension-ma
f=163-(12kg)(9.8m/s^2)
f=163-117.6
f=45.6
f=ma
45.6=12(a)
a=45.6/12
a=3.8m/s^2 downwards
Sorry, "Since there is tension in the rope we know the net force is in the opposite direction of gravity"
I meant the force of tension is upwards and the force of gravity downwards. The net force is downwards
Sorry - the net force is upwards. The tension in the rope upwards is greater than the weight of the bucket; hence the net force is upwards (as your own math shows). Thus the acceleration is upwards.Quote:
Originally Posted by Wuerschti
Yea that's what I meant, I just confused myself twice.
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