Welcome to the article The spring in a retractable ballpoint pen is 1 8 cm long with a 340 N m spring constant When the pen is retracted the. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
The total energy required to extend the pen is the sum of the energies for the initial compression and the additional compression of the spring. The energy required to extend the pen can be calculated using the formula for potential energy stored in a spring:
Potential Energy = (1/2) * k * x^2
where k is the spring constant and x is the displacement of the spring.
In this case, the spring constant is 340 N/m and the displacement of the spring is the sum of the initial compression of 1.0 mm (or 0.1 cm) and the additional compression of 5.0 mm (or 0.5 cm).
First, we need to convert the displacement to meters:
Initial displacement = 0.1 cm = 0.001 m
Additional displacement = 0.5 cm = 0.005 m
Now we can calculate the energy required for each displacement:
Energy for initial compression = (1/2) * 340 N/m * (0.001 m)^2
Energy for additional compression = (1/2) * 340 N/m * (0.005 m)^2
Finally, we can add these energies together to find the total energy required to extend the pen:
Total Energy = Energy for initial compression + Energy for additional compression
The total energy required to extend the pen is the sum of the energies for the initial band the additional compression of the spring. To calculate the energy required to extend the pen, we use the formula for potential energy stored in a spring, which depends on the spring constant and the displacement of the spring.
Given that the spring constant is 340 N/m and the displacement is the sum of the initial compression of 0.1 cm and the additional compression of 0.5 cm, we convert the displacements to meters. Then, we calculate the energy for each displacement using the formula. Finally, we add the energies together to find the total energy required.
This calculation step ensures that we accurately determine the energy needed to extend the pen based on the given spring constant and displacements.
Note: The above calculation assumes that the spring obeys Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
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Rewritten by : Brahmana