Two boxes with masses m1 = 3.0 kg and m2 = 7.0 kg are connected by a massless ro

Question

Two boxes with masses m1 = 3.0 kg and m2 = 7.0 kg are connected by a massless rope, which is put over a massless, frictionless pulley as shown in the figure below. The coefficient of kinetic friction between the incline and the boxes is 0.10 and the coefficient of static friction between the incline and the boxes is 0.15. The angles of the inclines with respect to the horizontal are ?1 = 45 and ?2 = 30 . Use g = 9.8 m/s2 and assume the incline is fixed in space.

a) Show that the system will have a nonzero acceleration if it is initially at rest. Find the magnitude and direction of the acceleration.

b) If the system moves 2.5 m (in the direction you found in part (a)), what is the work done by: (i) gravity on m1, (ii) the normal force on m1, (iii) friction on m1, (iv) gravity on m2, (v) the normal force on m2, (vi) friction on m2.

c) Using your results from part (b), what is the speed of the system after it has moved 2.5 m if it was initially at rest?

Explanation / Answer

(a)We resolve the force in the Directio along the inclined plane and perpendicular to it .
For mass M1
say tension in the string is T an it is moving with an acceleration a upward of the incline
M1gSin45 + uM1gCos45 + M1a = T --------------(1)
Now for Mass 2
M2gSin45 - uM2gCos45 - M2a = T -----------(2)
Equating equation 1 and 2 we get
a = 5.203 m/s2
(b) Work done by gravity on M1 = M1gSin45*2.5 = 51.97 J
Work done bynormal force = 0
Work done by friction force on M1 = uM1gCos45*2.5 = 5.197 J
Work done By gravity on M2 = M2gSin45*2.5 = 121.269 J
Work done by normal force = 0
Work done by friction force = uM2gCos45 = 4.851 J
(c) We know that
V2 = U2 + 2aS
V2 = 0 +2*5.203*2.5
V = 5.1 m/s

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