5.(20 points) A block with mass m₁=5kg is attached to a block with mass m₂=8kg by a massless…

Step-by-step solution

1. 1. Work by Gravity

   $$W_g = m2 * g * d$$

   $$W_g = m_2gd$$

2. 2. Work by Friction

   W_f = -μk * N * d • N = m1 * g

   $$W_f = -\mu_k m_1gd$$

3. 3. Work by Spring

   $$W_s = -0.5 * k * d^2$$

   $$W_s = -\frac{1}{2}kd^2$$

4. 4. Net Work & KE

   W_net = W_g + W_f + W_s • ΔKE = 0.5 * (m1+m2) * v^2

   $$W_{net} = \frac{1}{2}(m_1+m_2)v^2$$

5. 5. Solve for Speed

   v = $\sqrt{2 * W_net / (m1+m2)}$

   $$v = \sqrt{\frac{2W_{net}}{m_1+m_2}}$$

6. 6. Yaad rakho / Key takeaway

   Use work-energy theorem when forces are variable or distance is given.

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