(25%) Problem 1: Three blocks are connected by ideal, meaning massless and inelastic, ropes which pass over ideal, meaning massless and frictionless, pulleys. Refer to the diagram provided. A blue block, with mass ma and located on a horizontal plank, is connected by a rope, with tension 71, to a red block, with mass my and dangling from the opposite end of the rope. The blue block is also connected by a second rope, with tension 72, to a green block, with mass m3 and located on a plank that is inclined by an angle 0 with the horizontal. When released from rest, or perhaps given a slight nudge, the system begins to accelerate with the red block descending towards the floor. MI Use ux and us for the coefficients of kinetic and static friction, respectively, between either block and its respective plank. In the notation for the forces given below, "horiz refers to the horizontal plank, and "slope" refers to the inclined plank. . Weights, if required, will be denoted with the corresponding subscript of the block as Fai, for i = 1, 2, 3. Snipping Tool . The normal force exerted by object a on object b, if required, will be denoted as F'n,a ,b NEW Mode Delay * X Cancel for a, b E {1, 2, 3, horiz, slope}, but a * b. Select the snip mode using the Mode button or click the . The force of kinetic friction exerted by object a on object b, if required, will be denoted button. as Fka b for a, be {1, 2, 3, horiz, slope}: but a # b. Snipping Tool is moving... . The force of static friction exerted by object a on object b, if required, will be denoted as In a future update, Snipping Tool will be moving to Fs,a b for a, be {1, 2, 3, horiz, slope} , but a * b. home. Try improved features and snip like usual wi & Sketch (or try the shortcut Windows logo kev + Shift + 5),Correct! # 80% Part (b) Please apply the interface below to draw your free body diagram for the blue block, with mass my. 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 r - y coordinate axes provided in the upper right-hand corner of the diagram in the problem statement. y Filhoriz .2 m2 TI / Correct! $ 8% Part (c) Please apply the interface below to draw your free body diagram for the green block, with mass my. 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 p' - y' coordinate axes provided near the left of the diagram in the problem statement. Feedback: is available. m3 Fk.slope -3 Snipping Tool8% Part (d) Because the three blocks are connected by ideal ropes, the magnitude of all three accelerations takes the same value, a. Enter a Cartesian unit-vector expression for the acceleration of the red block, the one with mass mi, with components defined according to the x - y coordinate axes displayed near the upper-right corner of the diagram in the problem statement. Grade Summary a = Deductions 0% Potential 100% 7 HOME Submissions 4 6 Attempts remaining: 3 4% per attempt) 3 detailed view END BACKSPACE CLEAR Hint Feedback I give up! Hints: 39% deduction per hint. Hints remaining: 1 Feedback: 3% deduction per feedback. 4 8% Part (e) Because the three blocks are connected by ideal ropes, the magnitude of all three accelerations takes the same value, a. Enter a Cartesian unit-vector expression for the acceleration of the blue block, the one with mass me, with components defined according to the x - y coordinate axes displayed near the upper-right corner of the diagram in the problem statement. 8% Part (f) Because the three blocks are connected by ideal ropes, the magnitude of all three accelerations takes the same value, a. Enter a Cartesian unit-vector expression for the acceleration of the green block, the one with mass ms, with components defined according to the c' - y' coordinate axes displayed on the left-hand side of the diagram in the problem statement. 8% Part (g) Enter an expression for the vertical component of the net force on the red block, the one with mass m , completing the expression of Newton's Second Law for that component. 8% Part (h) Enter an expression for the horizontal component of the net force on the blue block, the one with mass my, completing the expression of Newton's Second Law for that component. 8% Part (i) Enter an expression for the component of the net force on the green block, the one with mass my; that is parallel to and directed up the incline, completing the expression of Newton's Second Law for that component. 8% Part (j) Using the correct expressions for dj : dy, and d, that were obtained previously, eliminate all components of the accelerations in the Newton's Second Law expressions in favor of the common magnitude, a. (The challenge is to make the overall signs compatible.) After that, three equations remain with the unknowns 71, 72; and a. 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 m, =3.92 kg, my =3.16 kg, my =2.18 kg, 0 =58.7"; M =0.23, and #, =0.45? & 8% Part (k) Continuing with the same numeric values, my =3.92 kg: my =3.16 kg. my =2.18 kg, 0 =58.7", At =0.23, and /, =0.45, what is the tension, in newtons, in the rope that is connected to the red block? A 8% Part (1) Continuing with the same numeric values, my =3.92 kg, my =3.16 kg, my =2.18 kg, 0 =58.79, / =0.23, and us =0.45, what is the tension, in newtons, in the rope that is connected to the green block