Problem No 5 Based on Work Energy Principle WEP in Engineering Mechanics

TL;DR

Two springs with a stiffness of 0.5 N/cm are connected to a 5 kg ball, which falls from rest. The velocity of the ball after falling 15 cm is 1.683 m/s.

Transcript

hi friends we'll solve problem on work energy principle what is given in problem two springs each having stiffness of 0.5 newton per centimeter are connected to a ball having mass of 5 kg in a horizontal position producing an initial tension of 1.5 newton in each spring if the ball is allowed to fall from rest what will be its velocity after it has... Read More

Key Insights

• 💬 Two springs with an initial tension of 1.5 N and a stiffness of 0.5 N/cm are connected to a 5 kg ball.
• 🌸 The initial elongation of the springs is found to be 3 cm.
• 💦 The calculation of work done by spring forces takes into account the difference in initial and final deformations.
• 💬 The velocity of the ball after falling 15 cm is 1.683 m/s.
• 🌸 The number of springs in the problem affects how the work done by spring forces is calculated.
• 🏋️ The work done by weight is positive as the ball moves in the downward direction.
• 💦 The work energy principle is applied to determine the velocity of the ball after falling 15 cm.

Questions & Answers

Q: What are the initial tension and stiffness of the springs in the problem?

The initial tension in each spring is 1.5 N, and the stiffness of the springs is 0.5 N/cm.

Q: How is the initial elongation of the springs calculated?

Using the equation Fs = kx, where Fs is the spring force, k is the spring constant, and x is the deformation, the initial elongation of the springs is found to be 3 cm.

Q: What is the formula for calculating the work done by spring forces?

The formula is half of the spring constant (k) multiplied by the difference between the initial deformation (x1) squared and the final deformation (x2) squared.

Q: How is the velocity of the ball after falling 15 cm calculated?

By applying the work energy principle, where the work done by all forces (spring forces and weight) is equal to the change in kinetic energy, the velocity of the ball after falling 15 cm is calculated to be 1.683 m/s.

Summary & Key Takeaways

• Two springs with a stiffness of 0.5 N/cm are connected to a 5 kg ball in a horizontal position, creating an initial tension of 1.5 N in each spring.

• The ball is allowed to fall from rest, resulting in a 15 cm drop.

• By applying the work energy principle and calculating the work done by the spring forces and weight, the velocity of the ball after falling 15 cm is found to be 1.683 m/s.