Two boxes (24 kg and 62 kg) are being pushed across a horizontal frictionless surface, as the drawing shows. The 33-N pushing force P→ is horizontal and is applied to the 24-kg box, which in turn pushes against the 62-kg box. Find the magnitude of the force F→ that the 24-kg box applies to the 62-kg box.

Question

Physics

Guest

14 February, 08:51

Two boxes (24 kg and 62 kg) are being pushed across a horizontal frictionless surface, as the drawing shows. The 33-N pushing force P→ is horizontal and is applied to the 24-kg box, which in turn pushes against the 62-kg box. Find the magnitude of the force F→ that the 24-kg box applies to the 62-kg box.

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Answers (1)

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Dwayne Ferguson · Answer 1

23.8 N

Explanation:

Given that

Mass of the first box, m = 24 kg

Mass of the second box, M = 62 kg

Pushing force, F = 33 N

There is an acceleration, a in between the system and another force, f in between both blocks. Thus, we can say, using Newton's law

F - f = m. a

f = M. a

If we add both equations together, we have

F = m. a + M. a

F = (m + M) a

33 = (24 + 62) a, making a subject of formula, we have

a = 33 / 86

a = 0.384 m/s²

Recall, from the second equation,

f = M. a, now, if we substitute for both, we get

f = 62 * 0.384

f = 23.8 N

The magnitude of force the 24 kg applies to the 62 kg is 23.8 N