Question

7 a sphere x collides head on with a second identical sphere y which is stationary. the mass of each sphere is 0.15kg. sphere x is travelling at a velocity of 2.0m/s before the collision and produces an impulse of 0.21 ns on sphere y. what is the velocity of sphere x after collision? a 0.60m/s in the opposite direction to y b 0.60m/s in the same direction as y c 1.4m/s in the opposite direction to y d 1.4m/s in the same direction as y

Explanation:

Step1: Apply impulse - momentum theorem

Impulse \(J = \Delta p\). For sphere \(Y\), \(J = m\times v_Y - 0\) (initial momentum of \(Y\) is \(0\) as it is stationary). Given \(J = 0.21\space Ns\) and \(m=0.15\space kg\), then \(v_Y=\frac{J}{m}=\frac{0.21}{0.15}=1.4\space m/s\)

Step2: Apply conservation of momentum

Conservation of momentum: \(m\times u_X+m\times u_Y=m\times v_X + m\times v_Y\). Since \(u_Y = 0\), \(m = 0.15\space kg\) and \(u_X=2.0\space m/s\), we have \(0.15\times2.0+0=0.15\times v_X+0.15\times1.4\)

Step3: Solve for \(v_X\)

Divide the equation \(0.15\times2.0 = 0.15\times v_X+0.15\times1.4\) by \(0.15\) (since \(m
eq0\)). We get \(2.0=v_X + 1.4\). Then \(v_X=2.0 - 1.4=0.6\space m/s\). The direction of \(X\) is the same as the direction of \(Y\) (because the impulse on \(Y\) is in the direction of \(X\)'s initial motion)

Answer:

B. \(0.60\space m/s\) in the same direction as \(Y\)