Moderate -0.3 This is a standard two-string equilibrium problem requiring resolution of forces horizontally and vertically. Students apply routine techniques (resolving forces, using given angle and tension) with straightforward trigonometry and simultaneous equations. The problem is slightly easier than average as it's a textbook-style mechanics question with clear setup and no conceptual surprises, though it requires careful execution across multiple steps.
\includegraphics{figure_2}
A block of mass 15 kg hangs in equilibrium below a horizontal ceiling attached to two strings as shown in the diagram. One of the strings is inclined at \(45°\) to the horizontal and the tension in this string is 120 N. The other string is inclined at \(θ°\) to the horizontal and the tension in this string is \(T\) N. Find the values of \(T\) and \(θ\). [6]
Question 2:
2 | EITHER: | (M1 | Attempt to resolve (either direction with
correct number of terms and
dimensionally correct)
T sin θ + 120 sin 45 = 15g | A1 | Resolving vertically
T cos θ = 120 cos 45 | A1 | Resolving horizontally
( )
15g –120sin45
[tan θ =
( )
120cos45
or T = 65.152 +84.852 ] | M1 | For using division to find θ or for using
Pythagoras to find T
θ = 37.5 | A1
T = 107 | A1)
OR1:
120 T 15g
= =
sin ( 90+θ ) sin135 sin ( 135−θ ) | (A1 | One correct equation
A1 | A second correct equation
M1 | Attempt to solve for θ or T
θ = 37.5 | A1
T = 107 | A1
M1) | Attempt to use triangle of forces
Question | Answer | Marks | Guidance
OR2:
T 15g 120
= =
sin45 sin ( 45+θ ) sin ( 90−θ ) | (A1 | One correct equation
A1 | A second correct equation
M1 | Attempt to solve for θ or T
θ = 37.5 | A1
T = 107 | A1)
OR3:
[T2 = 1502 + 1202 – 2(150)(120) cos 45] | (M1 | Use cosine rule in a triangle with sides
120, 150 and T and with corresponding
angles 90 – θ, 45 + θ, 45
A1 | Correct equation
T = 107 | A1
M1 | Use sin rule or cosine rule in an attempt to
find θ
120/sin(90 – θ) = 106.97/sin 45 | A1 | A correct equation in θ such as this
θ = 37.5 | A1)
6
Question | Answer | Marks | Guidance
\includegraphics{figure_2}
A block of mass 15 kg hangs in equilibrium below a horizontal ceiling attached to two strings as shown in the diagram. One of the strings is inclined at $45°$ to the horizontal and the tension in this string is 120 N. The other string is inclined at $θ°$ to the horizontal and the tension in this string is $T$ N. Find the values of $T$ and $θ$. [6]
\hfill \mbox{\textit{CAIE M1 2017 Q2 [6]}}