Answer to Question #168721 in Physics for MJ

Question

A block of mass (m1 = 15 kg) on a rough, horizontal surface is connected to a ball of mass (m2 = 25 kg) by a lightweight cord over a light weight, frictionless pulley, as shown in Figure. A force of magnitude F = 40 N at an angle θ = 25º with the horizontal is applied to the block as shown and the block slides to the right. The coefficient of the kinetic friction between the block and the surface is uk = 0.18. Determine the magnitude of the acceleration of the two objects. 

Answer 1

$$N=m_1g-F\sin{\theta}\\N=(15)(9.8)-40\sin{25}=130\ N$$

$$(m_1+m_2)a=F\cos{\theta}-m_2g-F_f\\ (15+25)a=40\cos{25}-(25)(9.8)-(0.18)(130)\\a=5.8\frac{m}{s^2}$$