Question 42
A rod PQ is attached at P to a vertical wall, as shown in Fig. 3.1.
The length of the rod is 1.60 m. The weight W of the rod acts 0.64 m
from P. The rod is kept horizontal and in equilibrium by a wire attached to Q
and to the wall at R. The wire provides a force F on the rod of 44 N at 30° to
the horizontal.
(a) Determine
(i) the vertical component of F, [1]
(ii) the horizontal component of F. [1]
(b) By taking moments about P, determine the weight W of the rod. [2]
(c) Explain why the wall must exert a force on the rod at P. [1]
(d) On Fig. 3.1, draw an arrow to represent the force acting on the rod at
P. Label your arrow with the letter S. [1]
Reference: Past Exam Paper – June 2015 Paper 22 Q3
Solution:
(a)
(i) Vertical component = 44 sin 30° = 22 N
(ii) Horizontal component = 44 cos 30° = 38(.1)
N
(b)
{The vertical component of F acts at a distance of
(0.64 + 0.96 =) 1.60m from the pivot.
Clockwise moment = Anti-clockwise moment}
W × 0.64 = 22 × 1.60
W = 55 N
(c) F has a horizontal component (not balanced by
W)
{The horizontal component of F acts on the wall and
this is not balanced by W. From Newton’s 3rd law, there should be an
equal and opposite force exerted by the wall on the rod.}
OR F has 38 N acting horizontally
OR 38 N acts on wall
OR vertical component of F does not balance W
OR F and W do not make a closed triangle of forces
(d) Line from P in the direction towards the point
on wire vertically above W and direction up
{This force, along with F and W should form a system
that is in equilibrium. For equilibrium, the resultant force and the resultant
moment should be zero. If all the 3 forces pass through the same point, the
resultant moment would be zero.
Moment = Force × perpendicular distance from line
of action of force to pivot.
In this case, the pivot is that point where all the 3
forces pass. As they pass on the point, the ‘distance …’ is zero, and thus, the
moment at that point is zero.}
No comments:
Post a Comment
If it's a past exam question, do not include links to the paper. Only the reference.
Comments will only be published after moderation