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Simple Equilibrium

Equilibrium Problems

(See bottom of page for answers.)

1. An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the negative y direction. Find the magnitude of the third force acting on the object.


equilibrium is shown for a hanging object in which weight is cancelled by the tension on three ropes.

A 10-kg sign is suspended by three ropes, each supporting an equal portion of the sign's weight. The two end ropes make an angle of 70º to the horizontal. What is the tension on each of the ropes?

3. A 15 m rope is strung horizontally two poles. When a 47 kg mass is hung at the mid-point the rope sags 11°. What is the tension in the rope?

4. A 29 kg sign is supported by a vertical chain at each end. A strong wind blows and the chains make a 30 degree angle with the vertical. What force does each chain exert?

5. A 32.53 N light hangs at equilibrium from two cables at angles 78.3 and 60.2 with respect to the ceiling. What is the tension in the first cable?

6. Two blocks on a ramp are connected by a string and tied to a wall. The mass of the lower block is 1.0 kg; the mass of the upper block is 2.0 kg. Given that the angle of the incline is 31 degrees, find the tensions in (a) the string connecting the two blocks and (b) the string tied to the wall.

7. A lamp weighs 150 N and is supported equally by two wires that form an angle of 120 degrees with each other.
a. What is the tension in each of these wires?
b. If the angle between the wires is reduced to 90 degrees, what is the new tension in each wire?
c. As the angle between the wires decrease, what happens to the force in the wires?


Since net force is zero at equilibrium, the resultant of the forces is zero.


At equilibrium, since acceleration is zero, net force is zero. The resultant of the three forces is zero.
√(4.42 + 6.52) = 7.9
ø = tan-1( 4.4/6.5) = 34º

The third force is 7.9 N 146º from the positive x direction.

For solutions to all the problems on this page click here.

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