Question
D) x=0.342m E) x=-0.218m 9) A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20N/m If the amplitude of this motion is 030 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position? 0.00J B) 0.22 J C) 0.45 J D) 0.90 J E) 1.4 J
Solution
4.4
(252 Votes)
Dior
Professional · Tutor for 6 years
Answer
Here's the solution for question 9:**Understanding the Problem**The problem describes a ball oscillating on a spring. We're given the spring constant (k), the amplitude (A), and we're asked to find the kinetic energy (KE) when the ball is at its maximum displacement from equilibrium (which is equal to the amplitude).**Relevant Concepts*** **Conservation of Energy:** In a simple harmonic motion system like this (with no friction), the total mechanical energy is conserved. The total energy continuously switches between potential energy (PE) stored in the spring and kinetic energy (KE) of the ball.* **Potential Energy of a Spring:** PE = (1/2)kx² , where k is the spring constant and x is the displacement from equilibrium.* **Kinetic Energy:** KE = (1/2)mv², where m is the mass and v is the velocity.**Solution**1. **Energy at Maximum Displacement:** When the ball is at its maximum displacement (x = A = 0.30 m), its velocity is momentarily zero. Therefore, all the energy is stored as potential energy in the spring.2. **Calculate Potential Energy:** PE = (1/2)kA² = (1/2)(20 N/m)(0.30 m)² = 0.90 J3. **Kinetic Energy:** Since the velocity is zero at maximum displacement, the kinetic energy is 0 J.**Answer:** A) 0.00 J**Why other options are incorrect:*** **B, C, D, and E:** These options represent non-zero kinetic energies. At maximum displacement, the velocity and therefore the kinetic energy must be zero. All the energy is potential energy at this point.