Two boxes connected by a light horizontal rope are on a horizontal surface, as s

Question

Two boxes connected by a light horizontal rope are on a horizontal surface, as shown in the following figure. The coefficient of kinetic friction between each box and the surface is 0.30. One box (box B) has mass 4.91 kg , and the other box (box A) has mass m . A force F with magnitude 38 N and direction 53.1 above the horizontal is applied to the 4.91 kg box, and both boxes move to the right with an acceleration of a = 1.50 m/s2

Part A

What is the tension T in the rope that connects the boxes?

Part B

What is the mass m of the second box? Use the unrounded intermediate answers to calculate the final one.

Explanation / Answer

(a) For box B

equation of motion will be

F*cos(theta) - T - f = m*a

38*cos(53.1) - T - f = 4.91*1.50

f = 0.30*N

N = m*g - F*sin(53.1)

= 4.91*9.8 - 38*sin(53.1)

N = 17.73 N

f = 5.32 N

22.82 - T - 5.32 = 7.36

T = 10.14 N

(b) For box A

equation of motion will be

T - f = m*a

f = 0.3*g*m

10.14 - 2.94*m = 1.5*m

m = 2.28 kg

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