State what the principle of conservation of momentum says.
Show that the spring’s elastic potential energy at an extension of $8.0\,\text{cm}$ is $0.48\,\text{J}$. Fig. 2.2 shows how the tension $F$ varies with the extension $x$ of the spring. Block A has mass $4.0\,\text{kg}$ and block B has mass $6.0\,\text{kg}$. The two blocks are kept apart on a horizontal frictionless surface so that the spring is extended by $8.0\,\text{cm}$.
The blocks are released from rest together. When the spring’s extension becomes zero, block A has speed $v_A$ and block B has speed $v_B$. For the instant when the spring’s extension becomes zero, use conservation of momentum to show that $$\frac{\text{kinetic energy of block A}}{\text{kinetic energy of block B}} = 1.5.$
Use the information in part (b)(i) and part (b)(ii).1 to find the kinetic energy of block A. It may be assumed that the spring’s kinetic energy is negligible and that air resistance is negligible.
Show that the spring’s elastic potential energy at an extension of $8.0\,\text{cm}$ is $0.48\,\text{J}$.
The blocks are let go from rest at the same time. Once the spring’s extension is zero, block A moves with speed $v_A$ and block B with speed $v_B$. At the instant when the spring’s extension becomes zero, use conservation of momentum to show that $$\frac{\text{kinetic energy of block A}}{\text{kinetic energy of block B}} = 1.5.$
Use the information in (b)(i) and (b)(ii)1 to work out the kinetic energy of block A. You may assume that the spring’s kinetic energy is negligible and that air resistance is negligible.
The blocks are released at time $t = 0$. On Fig. 2.3, sketch a graph to show how the momentum of block A varies with time $t$ until the extension of the spring becomes zero. Numerical values of momentum and time are not required.