Calculating Power Output: A Physics Problem Solution

Hey guys! Today, let's dive into a fun physics problem about calculating power output. We'll break down a scenario where Awanita is lifting items onto a shelf and figure out how much power she's generating. So, grab your thinking caps, and let's get started!

Understanding the Problem: Awanita's Shelf-Lifting Task

So, we've got Awanita, who's placing some items on a shelf. This shelf is 200 cm above the ground. Awanita is exerting a force of 20 N to lift a box from the floor to the shelf, and she does this in 5 seconds. Our mission, should we choose to accept it, is to calculate Awanita's power output. The formula we'll be using is Power ( ${P}$) = Work ( ${W}$) / time ( ${t}$).

Breaking Down the Concepts: Power, Work, and Time

Before we jump into the calculations, let's quickly recap the key concepts involved. Power is the rate at which work is done or energy is transferred. Think of it as how quickly you can get something done. The unit for power is Watts (W). Work, in physics terms, is done when a force causes displacement. In our case, Awanita's force is causing the box to move upwards. Work is measured in Joules (J). Time, well, that's pretty straightforward – it's the duration over which the work is done, measured in seconds (s).

Step-by-Step Solution: Calculating Awanita's Power Output

Now, let's get our hands dirty with the calculations. Here’s how we can solve this problem step-by-step:

1. Calculate the Work Done ( ${W}$): Work is done when a force moves an object over a distance. The formula for work is:

   ${ W = F \times d }$

   Where:

   ${W}$ is the work done (in Joules) *
   ${F}$ is the force applied (in Newtons) *
   ${d}$ is the distance the object moves (in meters)

   In our problem:

   ${F = 20 \text{ N}}$ *
   ${d = 200 \text{ cm} = 2 \text{ m}}$ (We need to convert cm to meters)

   So,

   ${ W = 20 \text{ N} \times 2 \text{ m} = 40 \text{ J} }$

   Awanita does 40 Joules of work lifting the box.

2. Calculate the Power Output ( ${P}$): Now that we have the work done, we can calculate the power output using the formula:

   ${ P = \frac{W}{t} }$

   Where:

   ${P}$ is the power (in Watts) *
   ${W}$ is the work done (in Joules) *
   ${t}$ is the time taken (in seconds)

   In our problem:

   ${W = 40 \text{ J}}$ *
   ${t = 5 \text{ s}}$

   So,

   ${ P = \frac{40 \text{ J}}{5 \text{ s}} = 8 \text{ W} }$

   Therefore, Awanita's power output is 8 Watts.

The Answer: 8 Watts

Boom! We've cracked the code. Awanita's power output is 8 W. So, the correct answer is B. 8 W.

Why Other Options Are Incorrect: A Quick Look

Just to be thorough, let’s quickly see why the other options aren't correct:

• A. 4 W: This would be the answer if we divided the force by the time, but that doesn't give us power. Power is work done over time, not force over time.
• C. 40 W: This is the work done, but we need to divide it by the time to get power.
• D. 800 W: This is what you'd get if you multiplied the force, distance, and time. That's not the formula for power!

Real-World Applications: Power Output in Everyday Life

This kind of calculation isn't just for textbooks, guys. Understanding power output is super relevant in the real world. For example, engineers use these principles to design motors and engines. Athletes track their power output during training to optimize performance. Even understanding the power consumption of your household appliances involves these concepts. Think about it – a high-wattage appliance like a microwave uses more power than a low-wattage one like a light bulb.

Key Takeaways: Mastering Power Calculations

So, what have we learned today? Let's recap the key takeaways:

• Power is the rate at which work is done.
• The formula for power is ${ P = \frac{W}{t} }$ where ${W}$ is work and ${t}$ is time.
• Work is calculated as ${ W = F \times d }$ where ${F}$ is force and ${d}$ is distance.
• Units matter! Make sure to use consistent units (meters for distance, seconds for time, Newtons for force, Joules for work, and Watts for power).

Practice Makes Perfect: Try These Similar Problems

Want to solidify your understanding? Try these similar problems:

1. A weightlifter lifts a 100 kg barbell 2 meters in 3 seconds. What is their power output?
2. A motor does 5000 J of work in 10 seconds. What is the power of the motor?
3. A cyclist exerts a force of 50 N to travel 100 meters in 20 seconds. What is the cyclist's power output?

Work through these, and you'll be a power calculation pro in no time!

Conclusion: Power Up Your Physics Skills

Well, there you have it, guys! We've successfully calculated Awanita's power output and explored the concepts of power, work, and time. Remember, physics isn't just about formulas; it's about understanding how the world around us works. So keep asking questions, keep exploring, and keep powering up your physics skills!

If you found this helpful, give it a thumbs up and share it with your friends. And as always, if you have any questions, drop them in the comments below. Until next time, keep learning!