Consider the setup presented in the figure. All surfaces are frictionless, while the string and pulley are light. Determine the magnitude of the acceleration of the two blocks.

Step-by-step solution

The given wedge forms a triangle with sides 3 m , 4 m , and 5 m . Since 3^2 + 4^2 = 5^2 , it is a right-angled triangle with the right angle at the top vertex. Let ₁ be the angle of inclination of the left surface (length 3 m ) and ₂ be the angle of inclination of the right surface (length 4 m ). Using the geometric properties of the triangle, the altitude h to the base is given by equating the area: 1 2 3 4 = 1 2 5 h h = 12 5 m The sine of the angles of inclination are: ₁ = h 3 = 12/5 3 = 4 5 ₂ = h 4 = 12/5 4 = 3