Dynamics Question: Calculate Acceleration of Buckets

[Electron17]

Homework Statement

Two buckets of nails are hung one above the other and are pulled up to a roof by a rope. Each bucket has a mass of 5.0 kg. The tension in the rope connecting the buckets is 60 N. Calculate the acceleration of the buckets.

Homework Equations

F=ma
F(net)=F(A)+F(g)

The Attempt at a Solution

The first thing I did was add up the two masses of the two buckets to get 10.0 kg. Then, since F(net)=F(A)+F(g), I substituted to get ma=F(A)+mg. I then rearranged for acceleration to get a=F(A)+mg/m. I plugged in the values for a=60 N+(10.0 kg)(-9.81 m/s^2)/10 kg to get 3.8 m/s^2 [down]. The answer is 2.2 m/s^2 [up]. I did notice that if I were to use a value of 5 kg (the mass of a single bucket), I would get the right answer. I suppose my error may have something to do with the fact that the tension is between the buckets, but we have learned nothing about that yet and I might need a bit of information having to do with that.

Any help is greatly appreciated.

 

[dotman]

I suppose my error may have something to do with the fact that the tension is between the buckets, but we have learned nothing about that yet and I might need a bit of information having to do with that.

Any help is greatly appreciated.

Yeah, that's the trick. Since they tell you the tension is in the rope between the buckets, this force only acts on the bottom bucket-- hence, when you do your calculations, you can only include the bottom bucket. If you wanted to do it for both buckets, you would need to know the tension in the rope above the first bucket, which isn't given to you (although, if you wanted to, you could find it). In any event, the acceleration of both buckets will be the same, so you really don't care after finding the acceleration of the bottom bucket.

The mass of the top bucket will have no impact on the tension in the rope between them, so you don't want to include that mass in your acceleration calculation.

 

[ogb p]

Your approach to solving this problem is correct. However, there is a small error in your calculation. When you rearranged the equation a=F(A)+mg/m, you should have divided by the total mass of the system (10 kg) instead of just one bucket (5 kg). This is because the acceleration is acting on the entire system, not just one bucket.

The correct equation should be a=F(A)+mg/10 kg. When you plug in the values, you will get an acceleration of 2.2 m/s^2 [up]. This is the correct answer.

Regarding the tension between the buckets, you are correct in assuming that it plays a role in the acceleration. In this case, the tension is acting in the opposite direction of the acceleration, as it is pulling the buckets up. This means that the net force acting on the system is actually the difference between the tension and the weight of the buckets.

The correct equation for the net force would be F(net) = T - mg, where T is the tension and mg is the weight of the buckets.

I hope this helps clarify your understanding of the problem. Keep in mind that in future problems, you may encounter more complex situations where the tension between objects plays a significant role in the dynamics of the system. So it is important to always consider all the forces acting on the system and their directions.