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 4.81kg , and the other box (box A) has mass m . A force F with magnitude 39.8N and direction 53.1? above the horizontal is applied to the 4.81kg box, and both boxes move to the right with an acceleration of a = 1.50m/s2 .(Figure 1)

Part A

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

Express your answer to two significant figures and include the appropriate units.

Part B

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

Explanation / Answer

for box B:

equation of motion will be:

Fcos53.1 - T - f = 4.81a

f = .3*N

N = mg - Fsin53.1

N= 15.31N

f = 4.59 N

19.13 - T = 4.81a

a = 1.5

T = 11.92N

for A:

equation of motion will be

T - f = ma

f = .3*mg

11.92 - 2.94m = 1.5m

m = 2.68 kg

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