Physics 9702 · AS & A Level · Linear momentum and its conservation

Linear momentum and its conservation — practice question

Ball X travels across a horizontal frictionless surface and then collides with ball Y, as shown in Fig. 4.1. Ball X has mass $0.300\,\text{kg}$ and initial velocity $v_x$ at an angle of $60.0^\circ$ to line AB. Ball Y has mass $0.200\,\text{kg}$ and initial velocity $6.00\,\text{m s}^{-1}$ at an angle of $60.0^\circ$ to line AB. The two balls stick together in the collision and afterwards move along line AB, as shown in Fig. 4.2.
(a(i))[2]

Calculate, to three significant figures, the component of the initial momentum of ball Y perpendicular to line AB.

(a(ii))[1]

Using the component of the initial momentum of each ball perpendicular to line AB, calculate, to three significant figures, $v_x$.

(a(iii))[2]

Show that the speed of the two balls after the collision is $2.4\,\text{m s}^{-1}$.

(b(i))[3]

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.

(b(ii))[3]

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.

(ii.1)[3]

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.

(ii.2)[3]

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.

Worked solution & mark scheme

This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: Momentum relation $p = mv$ applied

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