- #1
eurekameh
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Is this answer wrong? I think they've made a mistake in the work done by the spring, which I think should be (1/2)(135)(0.5)^3?
Solve the Work-Energy Problem: Is There a Mistake?
- Thread starter eurekameh
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In summary, the work-energy problem is a concept in physics that relates work, energy, and motion of an object. To solve it, you need to know the distance, force, and angle involved, and use the formulas W = Fd cosθ and KE = 1/2mv². Common mistakes include not considering all forces, using incorrect units, and neglecting the angle. An example of solving the problem is provided, and some real-life applications include launching rockets, designing roller coasters, and optimizing performance in various fields.
Is this answer wrong? I think they've made a mistake in the work done by the spring, which I think should be (1/2)(135)(0.5)^3?
- #2
Steely Dan
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No, the potential energy of a spring is indeed [itex]U = \frac{1}{2} k x^2[/itex]. If you want to think of it as work, then know that the spring force is [itex]F = k x[/itex], so the work done is
[tex] W = \int F dx = \int k x dx= \frac{1}{2} k x^2,[/tex]
which is the same answer.
[tex] W = \int F dx = \int k x dx= \frac{1}{2} k x^2,[/tex]
which is the same answer.
FAQ: Solve the Work-Energy Problem: Is There a Mistake?
What is the work-energy problem?
The work-energy problem is a concept in physics that deals with the relationship between work, energy, and motion of an object. It states that the work done on an object is equal to the change in its kinetic energy.
How do you solve the work-energy problem?
To solve the work-energy problem, you need to know the distance the object has moved, the force applied, and the angle between the force and the displacement. Then, you can use the formula W = Fd cosθ to calculate the work done, and the formula KE = 1/2mv² to calculate the kinetic energy. Finally, equating the two values will give you the solution.
What are some common mistakes when solving the work-energy problem?
Some common mistakes when solving the work-energy problem include not considering the angle between the force and displacement, using the wrong units, and not accounting for all the forces acting on the object. It is important to carefully analyze the given information and use the correct formulas to avoid making these mistakes.
Can you provide an example of solving the work-energy problem?
Sure, let's say a 10 kg object is pushed with a force of 20 N at an angle of 30 degrees to the horizontal and moves a distance of 5 m. Using the formula W = Fd cosθ, we get W = (20 N)(5 m)cos(30) = 86.6 J. Next, using the formula KE = 1/2mv², we get KE = 1/2(10 kg)(v²) = 86.6 J. Solving for v, we get v = √(2(86.6 J)/(10 kg)) = 5.25 m/s. Therefore, the final speed of the object is 5.25 m/s.
What are some real-life applications of the work-energy problem?
The work-energy problem has many real-life applications, such as calculating the force needed to launch a rocket into space, determining the braking distance of a car, and designing roller coasters. It is also used in fields like engineering, sports, and transportation to optimize performance and efficiency.