Referring to the image to the right, the mass of block 1 is m1 = 3.4 kg while the mass of block 2 is m2 = 8.6 kg. The coefficient of friction between m1 and the inclined surface is μ = 0.31. The inclined surface is at an angle θ = 31° above the horizontal. Part A) Write an equation for the magnitude of this system's acceleration. Use the variables from the problem statement together with g for acceleration from gravity in order to write your equation.

Part (b) Calculate the magnitude of the system's acceleration in m/s2.

a= 4.14 m/s²

Explanation

We calculate the weight component parallel to the displacement of the block:

We define the x-axis in the direction of the inclined plane , 25° to the horizontal.

W= m*g   : Total block weight

Wx= W*sen25°= m*g* sen25°

We apply Newton's second law :

∑F = m*a (Formula 1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Problem development

We apply the formula (1) to calculate the acceleration of the block:

∑Fx = m*a

Wx = m*a

m*g* sen25°  = m*a  : We divide by m on both sides of the equation

g* sen25° = a

a = g* sen25° = 9.8* sen25° = 4.14 m/s²