Name: _______________________________
Static Equilibrium, Stability, Rope Walker – Practice
1. A uniform sphere of mass m = 0.85 kg and radius r = 4.2 cm is held
in place by a massless rope attached to a frictionless wall a distance L
= 8.0 cm above the center of the sphere.
A. Find the tension in the rope.
B. Find the force on the sphere from the wall.
2. A scaffold of mass 60 kg and length 5.0 m is supported in a horizontal position by a vertical
cable at each end. A window washer of mass 80 kg stands at a point 1.5 m from one end.
A. What is the tension in the nearer cable?
B. What is the tension the farther cable?
3. A 75 kg window cleaner uses a 10 kg ladder that is 5.0 m long. He places one end on the
ground 2.5 m from a wall, rests the upper end against a cracked window, and climbs the
ladder. He is 3.0 m up along the ladder when the window breaks. Neglect friction between
the ladder and window and assume that the base of the ladder does not slip. When the
window is on the verge of breaking:
A. What is the magnitude of the force on the window from the ladder?
B. What is the magnitude of the force on the ladder from the ground?
C. What is the angle (relative to the horizontal) of that force on the ladder?
4. The system to the right is in equilibrium, with the string in
the center exactly horizontal. Block A weighs 40 N, block B
weighs 50 N, and angle  is 35°.
A. Find tensions T1, T2 and T3.
B. Find the angle θ.
5. A uniform beam of weight 500 N and length 3.0 m is
suspended horizontally. On the left it is hinged to a
wall; on the right it is supported by a cable bolted to
the wall at distance D above the beam. The least
tension that will snap the cable is 1200 N.
A. What value of D corresponds to that tension?
B. To prevent the cable from snapping, should D be increased or decreased from that
value?
Solutions:
1. A. 9.4 N
B. 4.4 N
2. A. 8.4 x 102 N
B. 5.3 x 102 N
3. A. 2.8 x 102 N
B. 8.8 x 102 N
C. 109o with respect to the +x axis (71o w.r.t. the –x axis)
4. A. T1 = 49 N T2 = 28 N
T3 = 57 N
B.  = 29o
5. A. 0.64 m
B. Increased