Torque and Static Equilibrium Intro:
Force on extended bodies
Thus far we have concentrated on forces hat can be considered to act at the
center of amss of an object, and have treated the object as a point.
1. Equilibrium? A stick is shown that has only two forces acting
on it, of equal sizes and in the directions shown. (I have magically turned
gravity Off.) Is the stick in equilibrium? Explain your answer
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2. Rotating a Meter Stick
Hold the meter stick with your fingers at the 5 cm mark. Tie a string at the
95 cm mark (or close to it) and hang about 500 grams from this point. Use
a simple spring scale to measure the forces. NOTE: some of the balances read
in grams, so to get force convert the reading to kg and multiply by g = 9.8
N/kg. In all cases apply a pull to make the stick horizontal.
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(a) First pull directly at the 95 cm mark. What force is required? (b) Now pull at the 50 cm mark. What force is required? (c) Now pull at the 27.5 cm mark. What force is required? (d) Finally tie a string at the 50 cm mark and angle the spring balance so that the angle is 30°. What force is required? |
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3. Free Body diagram for an extended object
Consider a meter stick supported at the 20 cm mark, with a mass attached to
the left end.
Describe in words what you would observe to know that the stick is in static
equilibrium.
Draw a free body diagram for the meter stick, indicating all forces that act
on the stick.
4. Direction of Torque The dot
represents the axis of rotation.
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(a) For each force, A through E, tell whether the torque caused is clockwise, counterclockwise, or zero.
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(b) Assume all of the forces have the same magnitude. Rank the torques produced in order from largest to smallest (e.g., A>B=C>D=E).
(c) Draw a different axis of rotation located vertically above the one shown,
and almost at the top of the object. Again tell whether the torques are clockwise
or counterclockwise or zero.
5. An example
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A beam is attached to a wall with a hinge, and supported by a rope
as shown. The beam is uniform with a weight of 500 N. Find (b) the horizontal and vertical components of the hinge force on the beam. |
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