Question

Two masses m1 -
1.5 kg and m2 -
3.0 kg are connected by a
thin string running over a massless pulley. One of the masses
hangs from the string; the other mass slides on a 35 ramp
with a coefficient of kinetic friction -
k -
0.40 (Fig. 6.33).
What is the acceleration of the masses?

Answer 1

$m_2g-T=m_2a \;\;\;(i)\\ N=m_1g cosθ \\ f_k = \mu N = \mu m_1 g cosθ \\ T -m_1gsinθ - \mu m_1 g cos θ =m_1a \;\;\;(ii)$

Adding (i) and (ii):

$m_2g -m_1g sin θ = \mu m_1 g cos θ = (m_1 + m_2)a \\ a = \frac{3 \times 10 - 1.5 \times 10 sin 35 - 0.4 \times 1.5 \times 10 \times cos 35}{4.5} \\ = \frac{30-8.60-4.915}{4.5} \\ = 3.66 \;m/s^2$