Moderate -0.3 This is a straightforward 3-force equilibrium problem requiring resolution of forces in two perpendicular directions. Students must find the geometry (3-4-5 triangle gives angles), then resolve vertically and horizontally to find two tensions. While it requires multiple steps, the techniques are standard and the geometry is simple, making it slightly easier than average.
\includegraphics{figure_3}
A particle \(P\) of mass 0.3 kg is held in equilibrium above a horizontal plane by a force of magnitude 5 N, acting vertically upwards. The particle is attached to two strings \(PA\) and \(PB\) of lengths 0.9 m and 1.2 m respectively. The points \(A\) and \(B\) lie on the plane and angle \(APB = 90°\) (see diagram). Find the tension in each of the strings. [5]
Question 3:
3 | 4 3
T × +T × +0.3g =5
A 5 B 5 | M1 | Resolving vertically
3 4
T × =T ×
A 5 B 5 | M1 | Resolving horizontally
A1 | Both correct
M1 | Solve for T or T
A B
T =1.6N and T = 1.2 N
A B | A1
Alternative method for question 3
5−3 T T
= A = B
sin90 sin126.9 sin143.1 | M1 | Attempt one pair of Lami’s equations
M1 | Attempt a second pair of Lami equations
A1 | Equations all correct
M1 | Evaluate T or T
A B
T =1.6N and T = 1.2 N
A B | A1
Question | Answer | Mark | Guidance
3 | Alternative method for question 3
4 4
T =5cos36.9−3cos36.9=5× −3×
A 5 5 | M1 | Resolve along PA
3 3
TB=5cos53.1−3cos53.1=5× −3×
5 5 | M1 | Resolve along PB
A1 | Both correct
M1 | Evaluate T or T
A B
T =1.6N and T = 1.2 N
A B | A1
Alternative method for question 3
Forces 2N, T and T with angles 36.9 and 53.1
A B | M1 | Attempt to illustrate a triangle of forces
[T =2cos36.9, T = 2cos53.1]
A B | M1 | Use trigonometry in the triangle to find T and T
A B
A1 | Both correct
M1 | Solve for T or T
A B
T =1.6N and T = 1.2 N
A B | A1
5
Question | Answer | Mark | Guidance
\includegraphics{figure_3}
A particle $P$ of mass 0.3 kg is held in equilibrium above a horizontal plane by a force of magnitude 5 N, acting vertically upwards. The particle is attached to two strings $PA$ and $PB$ of lengths 0.9 m and 1.2 m respectively. The points $A$ and $B$ lie on the plane and angle $APB = 90°$ (see diagram). Find the tension in each of the strings. [5]
\hfill \mbox{\textit{CAIE M1 2019 Q3 [5]}}