CAIE M1 2009 June — Question 3

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2009
SessionJune
TopicNewton's laws and connected particles

3
\includegraphics[max width=\textwidth, alt={}, center]{af19f1e0-4cdf-407b-a0d6-cb0272066c30-2_492_606_1763_772} Forces of magnitudes \(7 \mathrm {~N} , 10 \mathrm {~N}\) and 15 N act on a particle in the directions shown in the diagram.
  1. Find the component of the resultant of the three forces
    (a) in the \(x\)-direction,
    (b) in the \(y\)-direction.
  2. Hence find the direction of the resultant.
    \includegraphics[max width=\textwidth, alt={}, center]{af19f1e0-4cdf-407b-a0d6-cb0272066c30-3_414_833_267_657} A block of mass 8 kg is at rest on a plane inclined at \(20 ^ { \circ }\) to the horizontal. The block is connected to a vertical wall at the top of the plane by a string. The string is taut and parallel to a line of greatest slope of the plane (see diagram).
  3. Given that the tension in the string is 13 N , find the frictional and normal components of the force exerted on the block by the plane. The string is cut; the block remains at rest, but is on the point of slipping down the plane.
  4. Find the coefficient of friction between the block and the plane.