Free Fall Work Problem: Lifting An 8N Object
Hey guys! Ever wondered about the work needed to lift an object back to its original position after it's been in free fall? Let's dive into a classic physics problem that explores this concept. We'll break down the steps, use some key physics principles, and solve it together. Get ready to flex those brain muscles and learn something cool!
Problem Statement
We have a body in free fall that takes 3 seconds to hit the ground. Its weight is 8 Newtons. The big question is: what work must be done to lift this body back to the exact spot it fell from? This is a super interesting problem because it combines concepts of free fall, gravity, and work. To tackle it, we'll need to dust off our understanding of these principles and apply them strategically.
Breaking Down the Problem
To solve this, we need to figure out a few things first. We know the time it takes to fall (3 seconds) and the weight of the object (8 N). Weight is crucial because it tells us the force due to gravity acting on the object. Remember, weight is the force exerted on an object due to gravity, and it's calculated as Weight = mass × acceleration due to gravity (g). The acceleration due to gravity (g) is approximately 9.8 m/s² on Earth. So, we can use the weight to find the mass of the object. Once we have the mass, we'll need to determine the height from which the object fell. For this, we'll use the equations of motion for free fall, specifically the one that relates distance, initial velocity, time, and acceleration. Since the object starts from rest, its initial velocity is zero, which simplifies our calculations. After finding the height, we can finally calculate the work done to lift the object back up. Work, in physics, is the energy transferred when a force moves an object over a distance. It's calculated as Work = Force × Distance. In this case, the force we need to apply is equal to the weight of the object (to counteract gravity), and the distance is the height we just calculated. So, let's get into the nitty-gritty of the calculations and see how it all comes together!
Step-by-Step Solution
1. Finding the Mass
As we discussed, weight is the force due to gravity, and it's given by the formula:
- W = m * g
Where:
- W = Weight (8 N)
- m = mass (what we want to find)
- g = acceleration due to gravity (approximately 9.8 m/s²)
Let's rearrange the formula to solve for mass (m):
- m = W / g
Now, plug in the values:
- m = 8 N / 9.8 m/s²
- m ≈ 0.816 kg
So, the mass of the object is approximately 0.816 kilograms. This is a crucial piece of information because it connects the force of gravity (weight) to the object's inertia (resistance to changes in motion). Knowing the mass helps us understand how the object will behave under the influence of forces, both during free fall and when we lift it back up.
2. Calculating the Height
Now that we have the mass, we need to find the distance the object fell. Since it was in free fall, we can use the following equation of motion:
- d = v₀ * t + (1/2) * g * t²
Where:
- d = distance (height, what we want to find)
- vâ‚€ = initial velocity (0 m/s since it starts from rest)
- t = time (3 s)
- g = acceleration due to gravity (9.8 m/s²)
Since the initial velocity (vâ‚€) is 0, the first term (vâ‚€ * t) becomes 0, simplifying the equation:
- d = (1/2) * g * t²
Plug in the values:
- d = (1/2) * 9.8 m/s² * (3 s)²
- d = (1/2) * 9.8 m/s² * 9 s²
- d = 4.9 m/s² * 9 s²
- d = 44.1 m
Therefore, the object fell from a height of 44.1 meters. This is a significant distance! Understanding how we arrived at this number is key. We used the fundamental principles of kinematics, specifically the equation of motion that describes the displacement of an object under constant acceleration. This equation allowed us to link the time of fall, the acceleration due to gravity, and the distance covered. Knowing this height is essential for the final step: calculating the work done.
3. Determining the Work Done
Finally, we can calculate the work needed to lift the object back to its original position. Work is done when a force causes displacement, and it's calculated as:
- W = F * d
Where:
- W = Work (what we want to find)
- F = Force (equal to the weight of the object, 8 N)
- d = distance (the height we calculated, 44.1 m)
Plug in the values:
- W = 8 N * 44.1 m
- W = 352.8 Joules
So, the work required to lift the object back to where it fell from is 352.8 Joules. That's it! We've successfully solved the problem by breaking it down into manageable steps. We first found the mass using the weight and the acceleration due to gravity. Then, we calculated the height using the equation of motion for free fall. Finally, we used the weight and the height to determine the work done. The unit of work, Joules, represents the amount of energy transferred or converted in the process. In this case, we're doing work against gravity to increase the object's potential energy.
Final Answer
The work that must be done to lift the body back to the place from where it fell is 352.8 Joules.
Key Takeaways
This problem beautifully illustrates the interplay between different concepts in physics. We saw how weight, mass, gravity, free fall, and work are all interconnected. Understanding these relationships is crucial for solving a wide range of physics problems. Here are some key takeaways:
- Free fall is a motion where the only force acting on an object is gravity.
- Weight is the force exerted on an object due to gravity.
- Work is the energy transferred when a force causes displacement.
- The equations of motion are powerful tools for analyzing motion under constant acceleration.
By breaking down complex problems into smaller, more manageable steps, we can apply the fundamental principles of physics to arrive at solutions. Remember, practice makes perfect, so keep exploring and tackling new challenges!
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