Applied Mathematics 144
Tutorial 10
3 October 2016
1. (a) Beam AB in panel (a) in the figure below rests on a smooth surface at point A and the
weight of the beam is negligible. There is a smooth hinge at point B. Draw a free body
diagram and show all the forces that act on the beam.
(b) The beam in panel (b) in the figure below has a smooth hinge and a weight of W . Draw
a free body diagram and show all the forces that act on the beam.
(c) The two spheres in panel (c) in the figure below have smooth surfaces and the contact
points with the container are also smooth. Isolate sphere A, which has a weight of 40 N,
and draw all the forces that act on sphere A.
2. The beam in panel (a) in the figure below has a smooth hinge at point A and a smooth
support at point B. Determine the reactions acting on the beam at the support points.
3. A smooth rod with a mass of 20 grams lie on a glass container as shown in panel (b) in the
figure below. Determine the reactions on the rod. (AB = 200 mm).
4. The indicated location of the centre of mass of the 1600-kg pickup truck is for the unladen
condition. If a load whose centre of mass is x = 400 mm behind the rear axle is added to the
truck, determine the mass mL of the load for which the normal forces under the front and
rear wheels are equal.
5. The 100 kg uniform beam AB is supported at A with a smooth hinge and at B and C by a
continuous cable that wraps around a frictionless pulley located at D. If a maximum tension
force of 800 N can be developed in the cable before it breaks, determine the greatest distance
d at which the 6-kN force can be placed on the beam. What are the horizontal and vertical
components of reaction at A just before the cable breaks?
6. The uniform 10-kg ladder rests on the rough floor for which the coefficient of static friction is
µ = 0.4 and against the smooth wall at B. Determine the horizontal force P the man must
exert on the ladder to cause it to move. (Hint: Assume the ladder is on the verge of slipping
and not tipping about point A).