Wood block 1 in (Figure 1), which has a mass of 1.0 kg, is at rest on a wood ramp. The angle of the ramp is 20º above horizontal. What is the smallest mass of block 2 that will start block 1 sliding uphill? Do not neglect friction. Please help I've been stuck on this for days...

Explanation:

For this problem we use the translational equilibrium condition. Our reference frame for block 1 is one axis parallel to the plane and the other perpendicular to the plane.

X axis

      -Aₓ - f_e +T = 0        (1)

Y axis

      N₁ - W_y = 0              ( 2)

let's use trigonometry for the weight components

      sin θ = Wₓ / W

      cos θ = W_y / W

      Wₓ = W sin θ

      W_y = W cos θ

We write the diagram for the second body.

Note that in the block the positive direction rd upwards, therefore for block 2 the positive direction must be downwards

      W₂ -T = 0                             (3)

we add the equations is 1 and 3

       - W₁ sin θ - μ N₁ + W₂ = 0

from equation 2

       N₁ = W₁ cos θ

we substitute

        -W₁ sin θ - μ (W₁ cos θ) + W₂ = 0

W₂ = m₁ g (without ea - very expensive)

This is the smallest value that supports the equilibrium system

layer a is the exosphere and layer b is the thermosphere.   is the answer i think but i hope this .