Problem Statement
A body of mass m₁ slides with velocity v₁ onto a platform of mass m₂ (initially at rest). Find the common final velocity and the heat generated by friction.
Given Information
- m₁ at v₁, m₂ at rest
- Friction until common velocity
Physical Concepts & Formulas
$$v_f=\frac{m_1v_1}{m_1+m_2},\quad Q=\frac{m_1m_2v_1^2}{2(m_1+m_2)}$$
Step-by-Step Solution
Step 1: Momentum conservation: v_f = m₁v₁/(m₁+m₂).
Step 2: Q = ΔKE = ½m₁v₁² − ½(m₁+m₂)v_f².
Step 3: Q = m₁m₂v₁²/[2(m₁+m₂)].
Worked Calculation
Q = m₁m₂v₁²/[2(m₁+m₂)]
Answer
$$\boxed{v_f=\frac{m_1v_1}{m_1+m_2},\quad Q=\frac{m_1m_2v_1^2}{2(m_1+m_2)}}$$
Physical Interpretation
Friction does negative work, converting kinetic energy to heat. The heat generated equals the CM-frame kinetic energy — independent of friction coefficient.
Leave a Reply