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Chapter 2

Q. 2.3

Determine the static deflection of the spring in the system of Figure 2.6(a).

Step-by-Step

Verified Solution

The FBDs of the system in its equilibrium position are shown in Figure 2.6(b). Summing forces to zero on the FBD of the left hand block \sum F=0 leads to

T_1+m_1g-k\Delta _s        (a)

Summing moments about the center of the disk leads to \sum M_\omicron =0, as

m_2gr_2-\left(m_1g-k\Delta_s \right)r_1= 0         (b)

from which the static deflection is determined as

\Delta _s=\frac{m_1gr_1 – m_2gr_2}{kr_1}          (c)