Question

A block with mass m1 = 4.50 kg and a ball with mass m2 = 7.70 kg are connected by a light string that passes over a frictionless pulley, as shown in figure (a). The coefficient of kinetic friction between the block and the surface is 0.300. 
(a) Find the acceleration of the two objects and the tension in the string. 
(b) Check the answer for the acceleration by using the system approach. (Use the following as necessary: m1, m2, μk, and g.) 
(c) What if an additional mass is attached to the ball? How large must this mass be to increase the downward acceleration by 60%? 

For (a) I calculated acceleration to be 5.10 m/s^2 and tension to be 36.2N. 
For (b) I the equation is a = (m2g-ukm1g)/(m1+m2) 
It is (c) that I cannot figure out. Can anybody please help me?

Answer 1

$1.6a = \frac{g(m_2 + m_3 - \mu km_1)}{m_1 + m_2 + m_3} \\ \\ 1.6a(m_1 + m_2 + m_3) = g(m_2 + m_3 - \mu km_1) \\ \\ (1.6a + \mu kg)m_1 + (1.6a - g)m_2 = (g - 1.6a)m_3 \\ \\ m_3 = \frac{1.6a +\mu kg}{g - 1.6a} m_1 - m_2 \\ \\ m_3 = 22.57 kg$