Three parcels are connected by ideal, meaning massless and inelastic, ropes which pass over ideal, meaning massless and frictionless, pulleys. Refer to the figure provided. A blue parcel, with mass m2m2 and located on a horizontal plane, is connected by a rope, with tension T1T1, to a red parcel, with mass m1m1 and dangling from the opposite end of the rope. The blue parcel is also connected by a second rope, with tension T2T2, to a green parcel, with mass m3m3 and located on a plane that is inclined by an angle ?? with the horizontal. When released from rest, or perhaps given a slight nudge, the system begins to accelerate with the red parcel descending towards the floor.

Use ?k?k and ?s?s for the coefficients of kinetic and static friction, respectively, between either parcel and its respective plane. In the notation for the forces given below, "horiz" refers to the horizontal plane, and "slope" refers to the inclined plane.

• Weights, if required, will be denoted with the corresponding subscript of the parcel as F?g,iF?g,i, for i=1,2,3i=1,2,3.
• The normal force exerted by object aa on object bb, if required, will be denoted as F?n,a?bF?n,a?b for a,b?{1,2,3,horiz,slope}a,b?{1,2,3,horiz,slope}, but a?ba?b.
• The force of kinetic friction exerted by object aa on object bb, if required, will be denoted as F?k,a?bF?k,a?b for a,b?{1,2,3,horiz,slope}a,b?{1,2,3,horiz,slope}, but a?ba?b.
• The force of static friction exerted by object aa on object bb, if required, will be denoted as F?s,a?bF?s,a?b for a,b?{1,2,3,horiz,slope}a,b?{1,2,3,horiz,slope}, but a?ba?b.

A-Please use the interface below to devise your free body diagram for the red parcel, with mass m1m1. Consult the problem statement with regard to notation. Components of the net force displayed in the lower-left corner of the FBD are relative to the x?yx?y coordinate axes provided in the upper right-hand corner of the figure in the problem statement.

B-Please use the interface below to devise your free body diagram for the blue parcel, with mass m2m2. Consult the problem statement with regard to notation. Components of the net force displayed in the lower-left corner of the FBD are relative to the x?yx?y coordinate axes provided in the upper right-hand corner of the figure in the problem statement.

C-Please use the interface below to devise your free body diagram for the green parcel, with massm3m3. Consult the problem statement with regard to notation. Components of the net force displayed in the lower-left corner of the FBD are relative to thex??y?x??y?coordinate axes provided near the left of the figure in the problem statement. D-Because the three parcels are connected by ideal ropes, the magnitude of all three accelerations takes the same value, aa. Input a Cartesian unit-vector expression for the acceleration of the red parcel, the one with mass m1m1, with components defined according to the x?yx?y coordinate axes displayed near the upper-right corner of the figure in the problem statement.

E-Because the three parcels are connected by ideal ropes, the magnitude of all three accelerations takes the same value, aa. Input a Cartesian unit-vector expression for the acceleration of the blue parcel, the one with mass m2m2, with components defined according to the x?yx?y coordinate axes displayed near the upper-right corner of the figure in the problem statement.

F-Because the three parcels are connected by ideal ropes, the magnitude of all three accelerations takes the same value, aa. Input a Cartesian unit-vector expression for the acceleration of the green parcel, the one with mass m3m3, with components defined according to the x??y?x??y? coordinate axes displayed on the left-hand side of the figure in the problem statement.

G-Input an expression for the vertical component of the net force on the red parcel, the one with mass m1m1, completing the expression of Newton's Second Law for that component.

H-Input an expression for the horizontal component of the net force on the blue parcel, the one with mass m2m2, completing the expression of Newton's Second Law for that component.

I- Input an expression for the component of the net force on the green parcel, the one with mass m3m3, that is parallel to and directed up the incline, completing the expression of Newton's Second Law for that component.

J-Using the correct expressions for a?1a?1, a?2a?2, and a?3a?3 that were obtained previously, eliminate all components of the accelerations in the Newton's Second Law expressions in favor of the common magnitude, aa. (The challenge is to make the overall signs compatible.) After that, three equations remain with the unknowns T1T1, T2T2, and aa. Solve for the acceleration, obtaining an expression that is independent of the tensions. What is the numeric value of the acceleration, in meters per squared second, if m1=m1=3.82kgkg, m2=m2=2.86kgkg, m3=m3=1.78kgkg, ?=?=66.5??, ?k=?k=0.12, and ?s=?s=0.39?

K-Continuing with the same numeric values, m1=m1=3.82kgkg, m2=m2=2.86kgkg, m3=m3=1.78kgkg, ?=?=66.5??, ?k=?k=0.12, and ?s=?s=0.39, what is the tension, in newtons, in the rope that is connected to the red parcel?

L-Continuing with the same numeric values, m1=m1=3.82kgkg, m2=m2=2.86kgkg, m3=m3=1.78kgkg, ?=?=66.5??, ?k=?k=0.12, and ?s=?s=0.39, what is the tension, in newtons, in the rope that is connected to the green parcel?