wo boxes of mass m 9 kg and m2 4 kg are touching and rest on a rough, horizontal

Question

wo boxes of mass m 9 kg and m2 4 kg are touching and rest on a rough, horizontal floor. The kinetic coefficient of friction is 0.20 and the static coefficient of friction is 0.30. a) If a force is applied to mi so that it pushes mi against m what value of force must be applied before both masses will move? 2 b) If a force of 45 N is applied to both boxes what will be their acceleration? y) v 13 c) What will be the force between the boxes? F12- How much kinetic energy will the two boxes have if this force is applied for a distance of 20c ON d)

Explanation / Answer

Here ,

m1 = 9 Kg

m2 = 4 Kg

u = 0.30

a) for the force applied on the mass m

Force needed = u * (m1 + m2) * g

Force needed = 0.30 * (9 + 4) * 9.8

Force needed = 38.22 N

b)

let the acceleration is a

Using second law of motion

F - uk * (m1 + m2) * g = (m1 + m2) * a

45 - 0.20 * 9.8 * (9 + 4) = (9 + 4) * a

solving for a

a = 1.51 m/s^2

the acceleration is 1.51 m/s^2

c)

force between the blocks is F

F = m2 * a + uk * m2 * g

F = 4 * (1.51 + 0.20 * 9.8)

F = 13.9 N

the force F is 13.9 N

d)

kinetic energy of two boxes = total work done

kinetic energy of two boxes = (45 - 0.20 * (9 + 4) * 9.8) * 0.20

kinetic energy of two boxes = 3.90 J

the kinetic energy of two boxes is 3.90 J

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