A non-uniform beam AD has weight W newtons and length 4 m - Edexcel - A-Level Maths Mechanics - Question 6 - 2014 - Paper 1
Question 6
A non-uniform beam AD has weight W newtons and length 4 m. It is held in equilibrium in a horizontal position by two vertical ropes attached to the beam. The ropes a... show full transcript
Worked Solution & Example Answer:A non-uniform beam AD has weight W newtons and length 4 m - Edexcel - A-Level Maths Mechanics - Question 6 - 2014 - Paper 1
Step 1
Find the distance of the centre of mass of the beam from A.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find the center of mass (d) of the beam AD, we consider the geometry of the beam. The distance can be computed by the moments about the point A:
The weighted mass of segment AB (1 m) is treated separately, and the contributions from AC (3 m) and AD must be considered as well.
The equation can be set up as:
T+2T+(W−3T)=W
Resolving this leads to the calculation of:
d=32m where m is mass derived from the weight W.
Step 2
an expression for the tension in the rope attached to B, giving your answer in terms of k and W.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Using the equilibrium of moments about point C:
The tensions in ropes at B (T_B) and C (T_C) can be modeled as:
TC=2TB
Setting up the moment equation:
TC⋅2=(kW−1)x
leads to:
TB=6(W⋅k−3k)
Step 3
the set of possible values of k for which both ropes remain taut.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To ensure both ropes are taut, we must satisfy:
The conditions TB≥0 and TC≥0, leading to:
0<k≤32 or 0<k<32 as the potential values of k.
