Standard +0.3 This is a straightforward M1 mechanics question involving resolution of forces and Newton's second law. Part (i) requires resolving forces vertically and horizontally to find P and the resultant, then applying F=ma - all standard techniques. Part (ii) is even more routine, requiring simple vector addition with one force horizontal. The question involves multiple steps but uses only basic mechanics concepts with no problem-solving insight required, making it slightly easier than average.
Particles P and Q, of masses m kg and 0.05 kg respectively, are attached to the ends of a light inextensible
string which passes over a smooth pulley. Q is attached to a particle R of mass 0.45 kg by a light inextensible
string. The strings are taut, and the portions of the strings not in contact with the pulley are vertical. P is in
contact with a horizontal surface when the particles are released from rest (see diagram). The tension in the
string QR is 2.52 N during the descent of R.
(i) (a) Find the acceleration of R during its descent. [2]
(b) By considering the motion of Q, calculate the tension in the string PQ during the descent of R. [3]
(ii) Find the value of m. [3]
R strikes the surface 0.5 s after release and does not rebound. During their subsequent motion, P does not
reach the pulley and Q does not reach the surface.
(iii) Calculate the greatest height of P above the surface. [8]
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A particle of mass $0.04$ kg is acted on by a force of magnitude $P$ N in a direction at an angle $\alpha$ to the upward vertical.
\begin{enumerate}[label=(\roman*)]
\item The resultant of the weight of the particle and the force applied to the particle acts horizontally. Given that $\alpha = 20°$ find
\begin{enumerate}[label=(\alph*)]
\item the value of $P$, [3]
\item the magnitude of the resultant, [2]
\item the magnitude of the acceleration of the particle. [2]
\end{enumerate}
\item It is given instead that $P = 0.08$ and $\alpha = 90°$. Find the magnitude and direction of the resultant force on the particle. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q6 [12]}}