A block with mass m1 = 8.5 kg is on an incline with an angle θ = 29.0° with respect to the horizontal. For the first question there is no friction, but for the rest of this problem the coefficients of friction are: μk = 0.26 and μs = 0.286.
1) When there is no friction, what is the magnitude of the acceleration of the block?
2) Now with friction, what is the magnitude of the acceleration of the block after it begins to slide down the plane?
3)To keep the mass from accelerating, a spring is attached. What is the minimum spring constant of the spring to keep the block from sliding if it extends x = 0.17 m from its unstretched length.
4)Now a new block with mass m2 = 14.6 kg is attached to the first block. The new block is made of a different material and has a greater coefficient of static friction. What minimum value for the coefficient of static friction is needed between the new block and the plane to keep the system from accelerating?
Answers & Comments
Verified answer
If you rotate the problem to where normal force is perpendicular to a axis, you will have a right triangle whose gravitational component is going southwest of the x axis
-----------------------mass-----
''
' "
' "
' "
'---------"
When there is no friction
f=ma = 8.5*9.8 = 83.3N this is the force for the gravity component of the triangle. SW
83.3cos61=adj= 40.4N
40.4N/8.5= 4.75m/s^2
the picture was supposed to be a triangle lmboooooo