Solve this Physics Problem

Question

In an inclined plane, the mass of block 1 is m1 = 3.0 kg, while the mass of block 2 is m2 = 6.0 kg. The coefficient of friction between m1 and the inclined surface is 𝜇k = 0.41. The inclined surface is at an angle θ = 37° above the horizontal. What is the acceleration of the system? (Enter the magnitude in m/s^2.)

Answer 1

Elle,

Assume the block descend with the 1st block in front of block 2. The net sliding force acting on the system "two blocks" would be F_sl=(m₁+m₂)gsinθ

The force slowing down their motion would come from the frictional force acting on block1 coming from a normal force

N=m₁gcosθ

times the friction coefficient μ_k

F_fr=μ_km₁gcosθ

Therefore the net force causing the system of two blocks with mass (m₁+m₂) descend is

F_net=F_sl-F_fr=(m₁+m₂)gsinθ-μ_km₁gcosθ

and the acceleration

a=F_net/(m₁+m₂)=gsinθ-μ_km₁gcosθ/(m₁+m₂)=

g{sinθ-μ_k[m₁/(m₁+m₂)]cosθ

The rest is to calculate a using the data given (make sure your calculator is in the mode "degrees" for angles)

Hope that is helpful

Dr.Ariel B