pls answer asap?

Question

a brick slides down an inclined plank at a constant speed when the plank is inclined at an angle theta_0. if the angle is increased to theta_1, the block accelerates down the plank with acceleration a. the coefficient of the kinetic friction is the same in both cases.
given the two theta, calculate a.

Answer 1

When the angle is θ1, the acceleration along the plane acting down is g sin θ1.

As the motion is uniform the frictional acceleration is - g sin θ1.


When the angle is θ2, the acceleration along the plane acting down is g sin θ2.

But the frictional acceleration is [- g sin θ1] and it remains the same for a range of
velocities.

http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html

The net acceleration is therefore a = g sin θ2 - g sin θ1
a = g [sin θ2 - sin θ1]

Answer 2

let's use x instead of theta

component of weight parallel to the inclined plank = frictional force
mgsin x0 = μmgcos x0 , μ = coefficient of kinetic friction
μ = tan x0

mgsin x1 - μmgcos x1 = ma
a = g(sinx1 - tan x0 cos x1)

Answer 3

gsinθ1 - μgcosθ1 = 0
gsinθ2 - μgcosθ2 = a
tanθ1 = μ
a = g(sinθ2 - tanθ1cosθ2)
or
a = gcosθ2(tanθ2 - tanθ1)