AP Physics C Mechanics 2.8: Spring Forces

Block 1 of mass $m_{1}$ is held at rest while compressing an ideal spring an amount $\Delta x$. The spring constant of the spring is k. Block 2 has mass $m_{2}$, where $m_{2}<m_{1}$. At time t=0, Block 1 is released. At time $t_{\mathrm{C}}$, the spring is no longer compressed and Block 1 immediately collides with and sticks to Block 2. The blocks stick together and the two-block system moves with constant speed v, as shown. Frictional effects are negligible.

After the experiment, the students use a balance to measure the mass of Block 2 and find it to be greater than what was determined in part (d). To explain this discrepancy, one of the students proposes that the spring constant was incorrectly measured at the beginning of the experiment. The students measure the spring constant again and record a new value, $k^{\prime}$.

Should the students expect that $k^{\prime}$ be greater than 150 N/m, less than 150 N/m, or equal to 150 N/m ? $k^{\prime}>150 \mathrm{~N} / \mathrm{m}$$k^{\prime}<150 \mathrm{~N} / \mathrm{m}$$k^{\prime}=150 \mathrm{~N} / \mathrm{m}$

Justify your answer.

Note: Figures not drawn to scale.

． A block of mass M is suspended from two identical springs of negligible mass，spring constant k and unstretched length L ．First，one spring is attached to the end of the other spring． The block is then attached to the end of the second spring and slowly lowered to its equilibrium position．The two springs stretch a total distance of $X_{1}$ ，as shown in Figure 1 above． Next，the springs are hung side by side．The block is attached to the end of the springs and again slowly lowered to its equilibrium position．The springs each stretch a distance of $X_{2}$ ，as shown in Figure 2 above．Which of the following equations correctly shows the relationship between $X_{1}$ and $X_{2}$ ？