Two-part friction scenarios

A question is this type if and only if it involves comparing two different configurations (e.g., force above vs below horizontal, or different angles) for the same object with friction.

6 questions · Standard +0.0

3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces
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CAIE M1 2009 November Q5
9 marks Moderate -0.3
5 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{efa7175f-832b-4cd3-82ab-52e402115081-3_317_517_922_468} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{efa7175f-832b-4cd3-82ab-52e402115081-3_317_522_922_1155} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} A small ring of weight 12 N is threaded on a fixed rough horizontal rod. A light string is attached to the ring and the string is pulled with a force of 15 N at an angle of \(30 ^ { \circ }\) to the horizontal.
  1. When the angle of \(30 ^ { \circ }\) is below the horizontal (see Fig. 1), the ring is in limiting equilibrium. Show that the coefficient of friction between the ring and the rod is 0.666 , correct to 3 significant figures.
  2. When the angle of \(30 ^ { \circ }\) is above the horizontal (see Fig. 2), the ring is moving with acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find the value of \(a\).
CAIE M1 2015 November Q6
10 marks Standard +0.3
6 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48f66bd5-33c1-4ce9-85f9-69faf10e871c-4_149_410_306_518} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48f66bd5-33c1-4ce9-85f9-69faf10e871c-4_133_406_260_1210} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} A small ring of mass 0.024 kg is threaded on a fixed rough horizontal rod. A light inextensible string is attached to the ring and the string is pulled with a force of magnitude 0.195 N at an angle of \(\theta\) with the horizontal, where \(\sin \theta = \frac { 5 } { 13 }\). When the angle \(\theta\) is below the horizontal (see Fig. 1) the ring is in limiting equilibrium.
  1. Find the coefficient of friction between the ring and the rod. When the angle \(\theta\) is above the horizontal (see Fig. 2) the ring moves.
  2. Find the acceleration of the ring.
OCR M1 2008 January Q6
16 marks Standard +0.3
6 A block of weight 14.7 N is at rest on a horizontal floor. A force of magnitude 4.9 N is applied to the block.
  1. The block is in limiting equilibrium when the 4.9 N force is applied horizontally. Show that the coefficient of friction is \(\frac { 1 } { 3 }\).

  2. [diagram]
    When the force of 4.9 N is applied at an angle of \(30 ^ { \circ }\) above the horizontal, as shown in the diagram, the block moves across the floor. Calculate
    1. the vertical component of the contact force between the floor and the block, and the magnitude of the frictional force,
    2. the acceleration of the block.
    3. Calculate the magnitude of the frictional force acting on the block when the 4.9 N force acts at an angle of \(30 ^ { \circ }\) to the upward vertical, justifying your answer fully.
OCR M1 2006 June Q5
11 marks Moderate -0.3
5 A block of mass \(m \mathrm {~kg}\) is at rest on a horizontal plane. The coefficient of friction between the block and the plane is 0.2 .
  1. When a horizontal force of magnitude 5 N acts on the block, the block is on the point of slipping. Find the value of \(m\).
  2. \includegraphics[max width=\textwidth, alt={}, center]{8ee41313-b516-48cb-bc87-cd8e54245d28-3_312_711_1244_758} When a force of magnitude \(P \mathrm {~N}\) acts downwards on the block at an angle \(\alpha\) to the horizontal, as shown in the diagram, the frictional force on the block has magnitude 6 N and the block is again on the point of slipping. Find
    1. the value of \(\alpha\) in degrees,
    2. the value of \(P\).
OCR M1 Q4
11 marks Moderate -0.3
\includegraphics{figure_4} A block of mass \(2\) kg is at rest on a rough horizontal plane, acted on by a force of magnitude \(12\) N at an angle of \(15°\) upwards from the horizontal (see diagram).
  1. Find the frictional component of the contact force exerted on the block by the plane. [2]
  2. Show that the normal component of the contact force exerted on the block by the plane has magnitude \(16.5\) N, correct to 3 significant figures. [2]
It is given that the block is on the point of sliding.
  1. Find the coefficient of friction between the block and the plane. [2]
The force of magnitude \(12\) N is now replaced by a horizontal force of magnitude \(20\) N. The block starts to move.
  1. Find the acceleration of the block. [5]
OCR M1 Q5
11 marks Standard +0.3
A block of mass \(m\) kg is at rest on a horizontal plane. The coefficient of friction between the block and the plane is \(0.2\).
  1. When a horizontal force of magnitude \(5\) N acts on the block, the block is on the point of slipping. Find the value of \(m\). [3]
  1. \includegraphics{figure_5ii} When a force of magnitude \(P\) N acts downwards on the block at an angle \(\alpha\) to the horizontal, as shown in the diagram, the frictional force on the block has magnitude \(6\) N and the block is again on the point of slipping. Find
    1. the value of \(\alpha\) in degrees,
    2. the value of \(P\).
    [8]