Particle on inclined plane

A question is this type if and only if it involves a particle on a rough or smooth inclined plane where you must resolve forces parallel and perpendicular to the plane to find acceleration, friction, normal reaction, or equilibrium conditions.

2 questions · Standard +0.3

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Edexcel M1 2013 June Q2
6 marks Standard +0.3
  1. the tension in the cable,
  2. the magnitude of the force exerted on the woman by the floor of the lift.
    \item \end{enumerate} \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{3c8dce6f-367a-42bb-be60-d03d0a23664f-04_616_780_118_584} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure} A box of mass 2 kg is held in equilibrium on a fixed rough inclined plane by a rope. The rope lies in a vertical plane containing a line of greatest slope of the inclined plane. The rope is inclined to the plane at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\), and the plane is at an angle of \(30 ^ { \circ }\) to the horizontal, as shown in Figure 1. The coefficient of friction between the box and the inclined plane is \(\frac { 1 } { 3 }\) and the box is on the point of slipping up the plane. By modelling the box as a particle and the rope as a light inextensible string, find the tension in the rope.
AQA Paper 2 2019 June Q17
9 marks Standard +0.3
17 Lizzie is sat securely on a wooden sledge.
The combined mass of Lizzie and the sledge is \(M\) kilograms.
The sledge is being pulled forward in a straight line along a horizontal surface by means of a light inextensible rope, which is attached to the front of the sledge. This rope stays inclined at an acute angle \(\theta\) above the horizontal and remains taut as the sledge moves forward.
\includegraphics[max width=\textwidth, alt={}, center]{838f0625-95e6-4ad4-b97b-3d3f77cc7f19-28_282_786_726_756} The sledge remains in contact with the surface throughout.
The coefficient of friction between the sledge and the surface is \(\mu\) and there are no other resistance forces. Lizzie and the sledge move forward with constant acceleration, \(a \mathrm {~ms} ^ { - 2 }\)
The tension in the rope is a constant \(T\) Newtons.
17
  1. Show that $$T = \frac { M ( a + \mu g ) } { \cos \theta + \mu \sin \theta }$$ 17
  2. It is known that when \(M = 30 , \theta = 30 ^ { \circ }\), and \(T = 40\), the sledge remains at rest.
    Lizzie uses these values with the relationship formed in part (a) to find the value for \(\mu\) Explain why her value for \(\mu\) may be incorrect.
    \includegraphics[max width=\textwidth, alt={}, center]{838f0625-95e6-4ad4-b97b-3d3f77cc7f19-30_2488_1719_219_150}
    \includegraphics[max width=\textwidth, alt={}, center]{838f0625-95e6-4ad4-b97b-3d3f77cc7f19-31_2488_1719_219_150}
    \includegraphics[max width=\textwidth, alt={}, center]{838f0625-95e6-4ad4-b97b-3d3f77cc7f19-32_2496_1721_214_148}