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Sloan [31]
2 years ago
6

Consider a force of 57.3 N, pulling 3 blocks of

Physics
1 answer:
andrezito [222]2 years ago
3 0

Block 1 (the rightmost block) has

• net horizontal force

∑ <em>F</em> = <em>F</em> - <em>T₁</em> - <em>f₁</em> = <em>m₁a</em>

• net vertical force

∑ <em>F</em> = <em>N₁</em> - <em>m₁g</em> = 0

where <em>F</em> = 57.3 N, <em>T₁</em> is the tension in the string connecting blocks 1 and 2, <em>f₁</em> is the magnitude of kinetic friction felt by block 1, <em>m₁</em> = 0.8 kg is its mass, <em>a</em> is the acceleration you want to find, and <em>N₁</em> is the magnitude of the normal force exerted by the surface.

Block 2 (middle) has much the same information:

• net horiz. force

∑ <em>F</em> = <em>T₁</em> - <em>T₂</em> - <em>f₂</em> = <em>m₂a</em>

• net vert. force

∑ <em>F</em> = <em>N₂</em> - <em>m₂g</em> = 0

with similarly defined symbols.

The same goes for block 3 (leftmost):

• net horiz. force

∑ <em>F</em> = <em>T₂</em> - <em>f₃</em> = <em>m₃a</em>

• net vert. force

∑ <em>F</em> = <em>N₃</em> - <em>m₃g</em> = 0

We have <em>m₁</em> = <em>m₂</em> = <em>m₃</em> = 0.8 kg, so I'll just replace each with <em>m</em>. It follows that each normal force has the same magnitude, <em>N₁</em> = <em>N₂</em> = <em>N₃</em> = <em>mg</em>. And as a consequence of that, each frictional force has the same magnitude, <em>f₁</em> = <em>f₂</em> = <em>f₃</em> = 0.4<em>mg.</em>

In short, the relevant equations are

[1] … 57.3 N - <em>T₁</em> - 0.4<em>mg</em> = <em>ma</em>

[2] …<em>T₁</em> - <em>T₂</em> - 0.4<em>mg</em> = <em>ma</em>

[3] … <em>T₂</em> - 0.4<em>mg</em> = <em>ma</em>

<em />

Adding [1], [2] and [3] together eliminates the tension forces, and we get

57.3 N - 1.2<em>mg</em> = 3<em>ma</em>

<em />

Solve for <em>a</em> :

57.3 N - 1.2 (0.8 kg) (9.8 m/s²) = 3 (0.8 kg) <em>a</em>

57.3 N - 9.408 N = (2.4 kg) <em>a</em>

<em>a</em> = (47.892 N) / (2.4 kg)

<em>a</em> ≈ 20.0 m/s²

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