Horizontal force only - find mass or coefficient

A question is this type if and only if it involves a block at rest on a rough horizontal surface with only horizontal applied force(s), and asks to find the mass of the block or coefficient of friction from limiting equilibrium conditions.

3 questions · Easy -1.3

3.03t Coefficient of friction: F <= mu*R model
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Edexcel Paper 3 2024 June Q1
3 marks Easy -1.3
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{184043b7-1222-44fb-bc9f-3f484f72147b-02_108_997_242_534} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a particle \(P\) of mass 0.5 kg at rest on a rough horizontal plane.
  1. Find the magnitude of the normal reaction of the plane on \(P\). The coefficient of friction between \(P\) and the plane is \(\frac { 2 } { 7 }\) A horizontal force of magnitude \(X\) newtons is applied to \(P\).
    Given that \(P\) is now in limiting equilibrium,
  2. find the value of \(X\).
CAIE M1 2023 November Q4
7 marks Moderate -0.8
A particle \(P\) of mass 0.2 kg lies at rest on a rough horizontal plane. A horizontal force of 1.2 N is applied to \(P\).
  1. Given that \(P\) is in limiting equilibrium, find the coefficient of friction between \(P\) and the plane. [3]
  2. Given instead that the coefficient of friction between \(P\) and the plane is 0.3, find the distance travelled by \(P\) in the third second of its motion. [4]
AQA Paper 2 2019 June Q11
1 marks Easy -1.8
A wooden crate rests on a rough horizontal surface. The coefficient of friction between the crate and the surface is 0.6 A forward force acts on the crate, parallel to the surface. When this force is 600 N, the crate is on the point of moving. Find the weight of the crate. Circle your answer. [1 mark] 1000 N \quad 100 kg \quad 360 N \quad 36 kg