Moderate -0.8 This is a standard two-string equilibrium problem requiring resolution of forces in two directions and solving simultaneous equations. It's straightforward application of basic statics with no conceptual challenges—easier than average but not trivial due to the calculation steps involved.
\includegraphics{figure_2}
A particle \(P\) of mass \(1.6\) kg is suspended in equilibrium by two light inextensible strings attached to points \(A\) and \(B\). The strings make angles of \(20°\) and \(40°\) respectively with the horizontal (see diagram). Find the tensions in the two strings. [6]
Question 2:
2 | M1 | Resolve forces horizontally
and/or vertically
T sin 20 + T sin 40 = 16
A B | A1 | Correct vertical equation
T cos 20 = T cos 40
A B | A1 | Correct horizontal equation
M1 | Attempt to solve for T and/or T
A B
T = 14.2N
A | A1 | T = 14.1528...
A
T = 17.4N
B | A1 | T = 17.3610...
B
Total: | 6
Alternative method for Question 2
M1 | Attempt to use Lami’s Theorem
16 T
= A
sin120 sin130 | A1
16 T
= B
sin120 sin110 | A1
M1 | Attempt to solve for T and/or T
A B
T = 14.2N
A | A1
T = 17.4N
B | A1
Total: | 6
Question | Answer | Marks | Guidance
\includegraphics{figure_2}
A particle $P$ of mass $1.6$ kg is suspended in equilibrium by two light inextensible strings attached to points $A$ and $B$. The strings make angles of $20°$ and $40°$ respectively with the horizontal (see diagram). Find the tensions in the two strings. [6]
\hfill \mbox{\textit{CAIE M1 2017 Q2 [6]}}