A 3-kg bucket is being pulled upwards by a cord. The tension in the cord is 35 N. What is the acceleration of the bucket? (The mass of the cord is negligible, which means you can assume m cord = 0.)

Hey, guys. So let's check out this problem here. We've got this 3 kilogram bucket that's being pulled up by a cord. So what that means here is we have this little box and it's being pulled up by a string like this. What we wanna do is we actually wanna figure out the acceleration of the buckets if we know the tension. Alright? So what we wanna do is we basically wanna figure out what a is equal to. That's the acceleration. So to do that, I know I'm gonna have to use f equals m a, but first, I'm gonna draw a free body diagram. So let's go ahead and do that first. I've got this little dot like this. Remember, I'm gonna check for the weight force first. That's w equals mg that acts downwards, then any applied forces or tensions. There's nothing directly pushing or pulling this, but I do know that the string is gonna exert some tension like this. And I actually know that tension is 35. So I don't have any applied forces. And then because this thing is basically in the air, there's no contact forces, so there's no normal or friction. So that's basically our free body diagram. Now we just get into our f equals ma. So step 2, we're gonna write our F equals ma. And so in order to expand our sum of all forces, we just have to pick a direction of positive. And that's just gonna be upwards. That's what we normally choose. So now we just expand out our forces, right? Our tension points longer direction of positive, so it's positive, And there are mg points downwards, so it picks up a minus sign. And so if we're trying to figure out the acceleration here, our a, we're gonna have to figure out everything else about this problem. So we need to know the mass, which we know, little g, which we know, and we also need the tension force, which we know. So we could just go ahead and plug in everything and then solve for a. So you're gonna get 35 minus 3 times 9.8 is equal to 3 times a. If you go ahead and simplify the left side, you're gonna get 5.6 equals 3 a, and so you simplify and you're gonna get 1.9 meters per second squared for the acceleration. Alright? So we look through our answer choices. They're all positive, so we don't have to worry about directions or anything like that. But we do have 1.9 that's right here. And because we've got a positive number, what this means is that the acceleration really just points along our direction of positive, which is up. And that makes some sense because the tension is 35. But if you were to work out the m g, which is downwards, what you would get is you would get 29.4. That's what you get when you do 3 times 9.8. So this force is bigger, the upward force. You're pulling it up stronger than gravity pulls it down. So it's gonna accelerate up. That's it for this one, guys. Let me know if you have any questions.

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A 3-kg bucket is being pulled upwards by a cord. The tension in the cord is 35 N. What is the acceleration of the bucket? (The mass of the cord is negligible, which means you can assume mcord = 0.)

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A 3-kg bucket is being pulled upwards by a cord. The tension in the cord is 35 N. What is the acceleration of the bucket? (The mass of the cord is negligible, which means you can assume m_cord = 0.)