Question

A ball with $10^3J$ of kinetic.energy coflides with a.hodzontally mounted spring. If the maximum compression of the. spring is 50 cm, then the spring constatrt of the spring is

• A. $2 x 10^3 Nm^{-1 }$
• B. $6 x 10^3 Nm^{-1 }$
• C. $8 x 10^3 Nm^{-1 }$
• D. $5 x 10^3 Nm^{-1 }$
• E. $3 x 10^3 Nm^{-1 }$

Answer 1

The Correct Option is C

We are given the following information:

• Kinetic energy of the ball = \( 10^3 \, \text{J} \) 
• Maximum compression of the spring = 50 cm = 0.5 m

When the ball collides with the horizontally mounted spring, its kinetic energy is completely converted into potential energy stored in the spring. The potential energy stored in the spring at maximum compression is given by: \[ E_{\text{spring}} = \frac{1}{2} k x^2 \] Where: - \( k \) is the spring constant, - \( x \) is the maximum compression of the spring (0.5 m). Since all the kinetic energy is transferred to the spring, we equate the kinetic energy to the potential energy stored in the spring: \[ 10^3 \, \text{J} = \frac{1}{2} k (0.5)^2 \] Solving for \( k \): \[ 10^3 = \frac{1}{2} k (0.25) \] \[ 10^3 = 0.125 k \] \[ k = \frac{10^3}{0.125} = 8 \times 10^3 \, \text{N/m} \]

Correct Answer:

Correct Answer: (C) \( 8 \times 10^3 \, \text{N/m} \)