**Problem 4:**A 6.00 kg iron ball moves at 2.75 m/s. How fast must a 2.65 g steel ball move so that the two balls have the same kinetic energy?---To solve this problem, we start by recognizing that the kinetic energy (\( KE \)) of an object is given by the formula:\[ KE = \frac{1}{2} m v^2 \]where:- \( m \) is the mass of the object,- \( v \) is the velocity of the object.### Given:- Mass of iron ball (\( m_1 \)) = 6.00 kg- Velocity of iron ball (\( v_1 \)) = 2.75 m/s- Mass of steel ball (\( m_2 \)) = 2.65 g = 0.00265 kg (conversion from grams to kilograms)### Objective:Find the velocity (\( v_2 \)) of the steel ball needed for it to have the same kinetic energy as the iron ball.### Solution Steps:1. Calculate the kinetic energy of the iron ball: \[ KE_1 = \frac{1}{2} m_1 v_1^2 = \frac{1}{2} \times 6.00 \, \text{kg} \times (2.75 \, \text{m/s})^2 \]2. Set the kinetic energy of the steel ball equal to the kinetic energy of the iron ball and solve for \( v_2 \): \[ KE_2 = \frac{1}{2} m_2 v_2^2 = KE_1 \] \[ \frac{1}{2} \times 0.00265 \, \text{kg} \times v_2^2 = KE_1 \]3. Rearrange to solve for \( v_2 \): \[ v_2^2 = \frac{2 \times KE_1}{0.00265} \] \[ v_2 = \sqrt{\frac{2 \times KE_1}{0.00265}} \]This setup provides a clear pathway to finding the velocity \( v_2 \), ensuring both balls have equal kinetic energy.

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Answered: 4. A 6.00 Kg iron ball moves at 2.75…

4. A 6.00 Kg iron ball moves at 2.75 m/s. How fast must a 2.65 g steal ball move so that the two balls have the same kinetic energy?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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