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Figure 1 Figure 2 1. (7 points, suggested time 13 minutes) Block A of mass $2 M...

May 16, 2024

Solution

Use Newton's Second Law to derive the initial acceleration of the two-block system at

t=t_{0}

. The net force on the system is due to the spring force, which is given by Hooke's Law:

F = -k_0 \Delta x

. Here,

\Delta x = \frac{1}{2}d

. Therefore, the force exerted by the spring is

F = -k_0 \left(\frac{1}{2}d\right) = -\frac{1}{2}k_0 d

According to Newton's Second Law,

F = ma

. The total mass of the system is

2M + M = 3M

. Thus, the initial acceleration

a

of the system is given by:

a = \frac{F}{m} = \frac{-\frac{1}{2}k_0 d}{3M} = -\frac{k_0 d}{6M}

Answer

a = -\frac{k_0 d}{6M}

Key Concept

Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation:

F = ma

(Net force equals mass times acceleration)

Explanation

By applying Newton's Second Law to the system and considering the force exerted by the spring, we can derive the initial acceleration of the two-block system.