Calculate, to three significant figures, the component of the initial momentum of ball Y perpendicular to line AB.
Using the component of the initial momentum of each ball perpendicular to line AB, calculate, to three significant figures, $v_x$.
Show that the speed of the two balls after the collision is $2.4\,\text{m s}^{-1}$.
The two balls keep moving together across the horizontal frictionless surface towards a spring, as shown in Fig. 4.3. They strike the spring and stay joined as they slow to a stop. All of the kinetic energy of the balls is changed into elastic potential energy of the spring. The energy $E$ stored in the spring is given by $E = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is its compression. The spring obeys Hooke’s law and has a spring constant of $72\,\text{N m}^{-1}$. Determine the maximum compression of the spring caused by the two balls.
On Fig. 4.4, sketch graphs showing how, as the compression $x$ changes from zero to maximum compression, (1) the magnitude of the deceleration $a$ of the balls, (2) the kinetic energy $E_K$ of the balls vary with $x$. Numerical values are not needed.
On Fig. 4.4, sketch graphs showing how, as the compression $x$ varies from zero to maximum compression, the magnitude of the deceleration $a$ of the balls changes with $x$. Numerical values are not required.
On Fig. 4.4, sketch graphs showing how, as the compression $x$ varies from zero to maximum compression, the kinetic energy $E_k$ of the balls changes with $x$. Numerical values are not required.