Consider FIG-DD in the appendix.   Note: For Blocks “A” & “B” & “C”: The mass of “A” is 30 kg.

• Positive x-axis points to the right,
• Positive y-axis points up,
• Angles are measured CCW (counter-clock-wise) from the positive x-axis.

When a numerical input is necessary:

• Enter your answer to 4 significant figures. Use a leading zero for numbers between -1 & 1.

• Do NOT use Scientific Notation.
• Angles must be reported with a minimum of 2 decimal places.
• Report directions as positive angles.  For instance, 350 degrees, not -10 degrees.
• Use the "standard" coordinate system unless noted otherwise.

• Regarding the magnitude of an angle between two objects that could be reported with more than one value, submit the smaller value. 
• Magnitude shall always be reported as a positive number.
• Value shall be reported either as a positive or negative number based upon the application.  When reporting a value, include the sign.

Problem-DD:

Consider FIG-DD in the appendix.

Note:

• For Blocks “A” & “B” & “C”:
  • The mass of “A” is 30 kg.
  • The mass of “B” is 50 kg.
  • The mass of “C” is 40 kg.
• Blocks “A” & “B” are in contact.
• Blocks “B” & “C” are in contact.
• Blocks “C” & “inclined plane” are in contact.
• The angle above the horizontal of the inclined plane is Θ = 30°.
• The static coefficients of friction:
  • Surface-1: 0.30
  • Surface-2: 0.40
  • Surface-3: 0.45
• The kinetic coefficients of friction:
  • Surface-1: 0.23
  • Surface-2: 0.37
  • Surface-3: 0.42

FIND:

• Calculate:
  • The maximum force of P, such that motion does not occur.
  • When this maximum P is applied, determine the remaining forces on the Blocks.

  • NOTE: Surface-3 is the surface between Block-C and the Inclined Plane.