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Investigation 1.2.1 Rotational Equilibrium Purpose To investigate the conditions necessary to prevent the rotation of a loaded beam
Procedure 1. Figure 1.2.13 shows you how to find the centre of gravity of a metre stick very quickly. Hold the metre stick on your two index fingers, as in the diagram. Slowly slide your fingers toward each other. When they meet, they will have the centre of gravity “surrounded.” Try this several times.
Figure 1.2.13
2. Mount your metre stick on a stand (Figure 1.2.14) with the pivot exactly at the centre of gravity. (Few metre sticks are perfectly uniform, so do not assume that the centre of gravity (CG) is at the 50.0 cm mark.) Adjust the pivot point precisely until the metre stick is in equilibrium. Record the position of the CG to the nearest millimetre.
3. Use a very thin, light piece of wire to attach a 1.00 kg mass at a distance of 20.0 cm from the pivot. The force of gravity on this mass will be 9.80 N. This force is labeled F1 on Figure 1.2.15. The distance from the pivot to the point where F1 acts is called the lever arm and is effect, labelled 1. The torque due to F1 produces a clockwise turning so it is called a clockwise torque. It is labelled 1 . ( 1 = F1 1).
CG pivot Figure 1.2.14
2
1 pivot
F2
F1
Figure 1.2.15
4. Suspend a 500 g mass by a light piece of wire on the other side of the metre stick. Adjust its lever armuntil the metre stick is in a state of equilibrium. The force of gravity on the 500 g mass is 4.90 N. Call this force F2 and its lever arm 2. The torque 2 is a counterclockwise torque. ( 2 = F2 l2) Record the forces and lever arms in a table like Table 1.2.2. Calculate the torques and enter them in the table for Trial 1. (Torque is expressed in N• m.) Table 1.2.2 Observations for Investigation 1.2.1
Trial
F1
l1
τ1
F2
l2
τ2
F3
l3
τ3
τ2 + τ3
(N)
(m)
(N•m)
(N)
(m)
(N•m)
(N)
(m)
(N•m)
(N•m)
1 2 3 4
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Chapter 1 Vectors and Static Equilibrium 25