Understanding Torque: A Key Concept in Physical Science

If a lighter child with a mass of 20 kg is sitting 3 meters from the center of a seesaw, how far from the center is a heavier child with a mass of 30 kg sitting?

• A. 1 m
• B. 2 m
• C. 4 m
• D. 5 m

Answer: (B)

To solve this problem, we need to apply the principle of torque in physics, which dictates that for a seesaw (or lever) to be balanced, the torques on either side must be equal. Torque is calculated as the product of the force (which, in this case, is the weight of the child, mass multiplied by the acceleration due to gravity) and the distance from the pivot point (the center of the seesaw). In this scenario, we will calculate the torques produced by both children around the center of the seesaw. For the lighter child weighing 20 kg and sitting 3 meters from the center, the torque would be: Torque from lighter child = mass × distance = 20 kg × 3 m For the heavier child with a mass of 30 kg, let’s denote the distance from the center as \(d\). The torque produced by this child would be: Torque from heavier child = mass × distance = 30 kg × d To achieve balance on the seesaw, the torques must equal each other: 20 kg × 3 m = 30 kg × d Now, solving for \(d\): 60 kg·m = 30 kg × d Dividing both sides

When you're studying for the UCF PSC1121 Physical Science Final Exam, understanding torque can really give you a leg up—especially when it comes to balancing problems like the seesaw example. So, let’s roll up our sleeves and simplify what torque means and how you can approach these problems effectively.

You remember those days in gym class, right? Where two kids would try to balance on a seesaw and inevitably end up flopping to one side or the other? Well, the balance doesn’t just happen by chance; there’s a whole physics principle behind it—torque. Basically, torque is all about rotational force and its relationship with distance. And trust me, once you grasp this, you’ll feel like a physics pro!

So, here’s the scenario: We’ve got a lighter kid weighing 20 kg sitting 3 meters from the center of the seesaw. On the flip side, we want to figure out how far the heavier child weighing 30 kg needs to sit to keep everything in balance. It sounds complicated, but once you break it down, it’s quite manageable.

To keep our seesaw balanced, the torques produced by both kids must be equal. Let’s put on our thinking caps: The torque can be figured out with this simple equation:

Torque = mass × distance from pivot

For our lighter child, placed 3 meters away, the torque works out to:

Torque from lighter child = 20 kg × 3 m = 60 kg·m.

Now, let’s look at the heavier child. We’re going to label their distance from the center as (d). The torque created by this child is:

Torque from heavier child = 30 kg × d.

To achieve equilibrium, we set those two torques equal to each other:

60 kg·m = 30 kg × d.

Here’s where it gets fun: solving for (d) is straightforward. Start by rearranging the equation:

1. 60 kg·m = 30 kg × d.

2. You divide both sides by 30 kg, and what do you get? It’s time for some division magic!

3. d = 60 kg·m / 30 kg.

And voila! You’re left with:

d = 2 m.

This means the heavier child needs to sit 2 meters from the center to balance out the seesaw. Easy, right?

Now, why does this matter? Well, understanding torque isn’t just about solving problems for exams; it’s a crucial principle in a lot of real-world applications—whether it’s designing bridges or understanding how gears work. The beauty of physics is that it’s everywhere around us, helping us understand the forces at play in our everyday lives.

So the next time you see a seesaw, just remember: balance isn't a random act; it's all about torque! Keeping that core principle in mind will not only help you ace your exam but will also unravel the magnificent world of physics that’s all around you.

To effectively prep for your UCF PSC1121 final exam, practicing problems like this one will hone your understanding of torque and related concepts, building a solid foundation for both your test and your future studies. Keep pushing through your revisions—you’ve got this!