Cambridge A Level Mechanics Practice Examination
Time 1 hour 15 minutes
Answer all the questions.
The use of an electronic calculator is expected, where appropriate.
Graph paper is given.
1. The diagram shows a uniform triangular lamina ABC with AB= 7 cm, BC = 24cm
and angle ABC = 90 degree. The lamina is pivoted a A so that it can rotate freely in a
vertical plane. The lamina is held in equilibrium, with BC horizontal and B vertically below A,
by means of a force of magnitude F Newtons acting a C perpendicular to AC and in the plane
of the lamina. The weight of the lamina is W (N) Newtons. Find F in terms of W. [4]
“ A lamina means an object that can be modeled by a plane region with no
thickness. A uniform lamina has constant mass per unit area.”
Since the lamina has constant mass, it would be necessary to find it's center of gravity
and then calculate the moments about the pivot point A, eliminating the reaction force
at point A.
“ A triangle doesn't have a center of symmetry.” The center of mass is at the point
where the three medians meet which is called the centroid. The median is the line
which joins the midpoint of that side to the opposite vertex. The use of a graph of the lamina,
with a suitable scale, will make finding it's midpoint easier.
, Solving for F(N): The perpendicular distance of W from Point A is 8 cm.
The perpendicular distance of F from point A is 25 cm.
Taking the moments of both forces about point A and setting them the equation to equal zero
(equilibrium condition) gives:
the force F is:
aws
Time 1 hour 15 minutes
Answer all the questions.
The use of an electronic calculator is expected, where appropriate.
Graph paper is given.
1. The diagram shows a uniform triangular lamina ABC with AB= 7 cm, BC = 24cm
and angle ABC = 90 degree. The lamina is pivoted a A so that it can rotate freely in a
vertical plane. The lamina is held in equilibrium, with BC horizontal and B vertically below A,
by means of a force of magnitude F Newtons acting a C perpendicular to AC and in the plane
of the lamina. The weight of the lamina is W (N) Newtons. Find F in terms of W. [4]
“ A lamina means an object that can be modeled by a plane region with no
thickness. A uniform lamina has constant mass per unit area.”
Since the lamina has constant mass, it would be necessary to find it's center of gravity
and then calculate the moments about the pivot point A, eliminating the reaction force
at point A.
“ A triangle doesn't have a center of symmetry.” The center of mass is at the point
where the three medians meet which is called the centroid. The median is the line
which joins the midpoint of that side to the opposite vertex. The use of a graph of the lamina,
with a suitable scale, will make finding it's midpoint easier.
, Solving for F(N): The perpendicular distance of W from Point A is 8 cm.
The perpendicular distance of F from point A is 25 cm.
Taking the moments of both forces about point A and setting them the equation to equal zero
(equilibrium condition) gives:
the force F is:
aws
