Answer to Question #187240 in Electrical Engineering for Kubilay

Question

The 25-kg block shown in figure moves on a plane with two attached springs. Determine the 

acceleration of the block at B using Force and acceleration. The spring1 has a stiffness k1 = 

200 N/m and unstretched length is 0.4 m. The spring2 has a stiffness k2 = 100 N/m and 

unstretched length is 0.7 m. The coefficient of kinetic friction between the crate and the plane 

is μk = 0.3.

Answer 1

$$ma=-F-\mu N+k_2\Delta x_2+k_1\Delta x_1\cos{30}\\ ma=-F-\mu (mg+k_1\Delta x_1\sin{30})\\+k_2\Delta x_2+k_1\Delta x_1\cos{30}$$

$$25a=-100-0.3(25(9.8)+(200)(0.8-0.4)\sin{30})\\+(100)(0.7-0.5)+(200)(0.8-0.4)\cos{30}$$

$$a=3.85\frac{m}{s^2}$$