User:Rosencrantz1/sandbox

$$m_1-m_2 = {m_1+m_2+m_p \over g}a + m_f$$ $$(m_1 - m_2 - m_f)g = (m_1 + m_2 + m_p)a$$ $$0.01271 = {0.11804 + m_p \over 9.81}$$ $$m_f$$ $$0.06781 - 0.05023 = 0.01271 \times 1.346 + m_f$$

$$E_p = mgh$$ $$E_k = {1 \over 2}mv^2$$ $$E_T = E_p + E_k $$ $$h = r(1 - cos{S \over R}) $$ $$195 (1 - cos{107 \over 200}) - 195 (1 - cos{93 \over 200}) = 6.54$$

$$\tau = I\alpha$$ $$\alpha = {a \over r}$$ $$\tau_N = \tau_T - \tau_f$$ $$\tau_N = rT = rm(g-a)$$ $$\tau_N = I\alpha + \tau_f$$ $$I = mr^2$$ $${I \over r^2} = {0.1950 \over 0.3410^2} = 1.6770$$