Static Equilibrium
For the system in equilibrium shown in the figure, determine the tension forces on the strings A
and B knowing that body C has 100 N.
A climber, with a mass of 70 kg, at a certain moment is stationary in the position shown in the figure.
Determine:
a) What is the magnitude of the tension in the rope?
b) What is the magnitude of the normal force exerted on the climber's feet?
A body with a mass of 200 kg is maintained in equilibrium on an inclined plane at 30° relative to the
horizontal by a cord passing through a fixed pulley and the other end supports a body with a mass
M. The rope makes with the inclined plane an angle of 45°. Determine:
a) The mass M;
b) The force exerted by the body on the plan.
A mass block m = 100 kg is suspended by the string system shown in the figure. Determine the
tension forces on all ropes.
Assume:
\( \sin 15°=0.259 \),
\( \cos 15°=0.966 \),
\( \sin 45°=0.707 \),
\( \cos 45°=0.707 \),
\( \sin 60°=0.866 \),
\( \cos 60°=0.5 \).
A body with weight W is suspended by a system of pulleys and ropes. Assuming these elements are
lightweight and the pulleys and ropes have no friction. Determine:
a) The force that man must apply to the rope to keep the body in static equilibrium;
b) If the rope is pulled down 60 cm, how much does the body be lifted?
Two identical spheres, A and B, are placed in a box. The line connecting the centers of
the two spheres makes an angle of 45° with the horizontal, and the reaction force exerted by the bottom
of the box on sphere B is 25 N. Determine the reaction force that the box exerts on the spheres at
the points of contact between the spheres and the box, and the force that sphere A exerts on
sphere B.
A body lies over an inclined plane of an angle α with the horizontal. To move upward it is required a force
parallel to the inclined plane whose minimum magnitude is F1 To prevent the body from
sliding down is required a force whose minimum magnitude is F2, also parallel to the slope.
If F1 = 2F2, calculate the coefficient of friction between the body and
the plane.
Three cylinders A, B, and C, with the horizontal axis and each weight W, are
in equilibrium on a system of two inclined planes, each with an angle of 30° relative to a plane, as
shown in the figure. Determine the magnitudes of reaction forces in each cylinder due to planes and
other cylinders.