6 A block rests on a horizontal surface. The coefficient of friction between the block and the surface is \(\mu\).
- Show that if the block is given an initial speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it will move a distance of \(\frac { \mathrm { v } ^ { 2 } } { 2 \mu \mathrm {~g} }\) before coming to rest.
Block B rests on the same horizontal surface as a sphere S . On the other side of S is a vertical wall, as shown below. The mass of \(B\) is 8 times the mass of \(S\).
\includegraphics[max width=\textwidth, alt={}, center]{b3e369f4-13f7-457b-9a43-04ed2e2a2bba-8_211_1013_662_244}
S is projected directly towards B with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and hits B . It is given that
- the coefficient of restitution between S and B is 0.8 ,
- collisions between S and the wall are perfectly elastic,
- the wall is perpendicular to the direction of motion of S and B .
Furthermore, you should model the contact between B and the surface as rough and model the contact between S and the surface as smooth. - Determine, in terms of \(u\), expressions for
- the speed of S
- the speed of B
immediately after the first collision between S and B . In each case stating the corresponding direction of motion.
It is given that B has sufficient time to come to rest before each subsequent collision with S .
Let \(\mathrm { X } _ { \mathrm { n } }\) be the distance B moves after the \(n\)th impact between S and B . - Explain why \(\mathrm { x } _ { \mathrm { n } + 1 } = \frac { 9 } { 25 } \mathrm { x } _ { \mathrm { n } }\).
- Given that \(u = 11.2\) and the coefficient of friction between B and the surface is \(\frac { 1 } { 7 }\), show that B will travel a total distance that cannot exceed 2.8 m .
\section*{END OF QUESTION PAPER}
\section*{OCR
Oxford Cambridge and RSA}