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A block with a mass of
30kg is located on a horizontal, frictionless tabletop. This block is connected by a rope to another block with a mass of
10kg. The rope is looped through a pulley on the table's edge so that the less massive block is hanging over the edge. What is the magnitude of the acceleration of the larger block across the table?

$3$ . A block with a mass of $30 \mathrm{~kg}$ is located on a horizontal, frictionless tabletop. This block is connected by a rope to another block with a mass of $10 \mathrm{~kg}$ . The rope is looped through a pulley on the table's edge so that the less massive block is hanging over the edge. What is the magnitude of the acceleration of the larger block across the table?

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q.

3

. A block with a mass of

30 \mathrm{~kg}

is located on a horizontal, frictionless tabletop. This block is connected by a rope to another block with a mass of

10 \mathrm{~kg}

. The rope is looped through a pulley on the table's edge so that the less massive block is hanging over the edge. What is the magnitude of the acceleration of the larger block across the table?

Identify Horizontal Force: Now, since the tabletop is frictionless, the only horizontal force acting on the $30$ kg block is the tension in the rope, which is equal to the force of gravity on the $10$ kg block ( $98$ N). We can use this force to find the acceleration of the $30$ kg block. $\newline$ Apply Newton's second law to the $30$ kg block: $\newline$ $F = ma$ $\newline$ $98$ N = $30$ kg $\times$ $a$ $\newline$ $10$ $0$ $\newline$ $10$ $1$ m/s $10$ $2$
Apply Newton's Second Law: Round the acceleration to two decimal places for the final answer: $\newline$ $a = 3.27 \, \text{m/s}^2$

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