Topic: Engineering Mechanics
A railway wagon A of mass 10000 kg collides with another identical wagon B as shown in the figure. If A is moving at 5 m/s and B is at rest at the time of collision, the maximum compression in the spring S with a spring constant of 2 MN/m will be
- A. 20 cm
- B. 30 cm
- C. 35 cm
- D. 45 cm
Answer: C. 35 cm
Explanation: For maximum compression, the calculation implies an inelastic collision where kinetic energy is converted into spring potential energy. Using the simplified energy equation provided: $\frac{1}{2} m_A v_A^2 = \frac{1}{2} kx²$. Substituting the values, we get $10000 \times 5^2 = 2 \times 10^6 \times x²$, which gives $x² = \frac{250000}{2000000} = 0.125$. Solving for $x$ yields $35.36$ cm, which is approximately 35 cm.