Inclined Planes

Why normal force between blocks is always zero irrespective of theta?(Friction is absent everywhere). $LaTeX$

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Comments

Suppose that the distance between the blocks remains zero, and that the acceleration of both blocks is the same. The normal force $N$ acts on the blocks equally and oppositely, per Newton's Third Law.

$m_1 \, g \, sin \theta + N = m_1 \, a \\ m_2 \, g \, sin \theta - N = m_2 \, a$

Adding both equations:

$(m_1 + m_2) \, g \, sin \theta = (m_1 + m_2) \, a \\ a = g \, sin \theta$

Plugging $a$ back into original equations:

$m_1 \, g \, sin \theta + N = m_1 \, g \, sin \theta \, \implies N = 0 \\ m_2 \, g \, sin \theta - N = m_2 \, g \, sin \theta \, \implies N = 0$

Steven Chase - 2 years, 10 months ago

@Rajdeep Dhingra @Steven Chase @Josh Silverman @Pranshu Gaba

Om Tiwari - 2 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$