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600 Unknown: L F
600 25 cm
Solve for the Unknown
Solve for the length of the lever arm L r sin (025 m)(sin 600 ) Substitute r 022 m Solve for the force Fr sin F r sin 35 N m (025 m)(sin 600 ) Substitute 35 N m, r 025 m, 600 025 m, 600 Math Handbook
Trigonometric Ratios page 855
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16 102 N Evaluate the Answer
Are the units correct Force is measured in newtons Does the sign make sense Only the magnitude of the force needed to rotate the wrench clockwise is calculated 8 Rotational Motion
11 Consider the wrench in Example Problem 1 What force is needed if it is applied to the wrench at a point perpendicular to the wrench 12 If a torque of 550 N m is required and the largest force that can be exerted by you is 135 N, what is the length of the lever arm that must be used 13 You have a 0234mlong wrench A job requires a torque of 324 N m, and you can exert a force of 232 N What is the smallest angle, with respect to the vertical, at which the force can be exerted 14 You stand on the pedal of a bicycle If you have a mass of 65 kg, the pedal makes an angle of 35 above the horizontal, and the pedal is 18 cm from the center of the chain ring, how much torque would you exert 15 If the pedal in problem 14 is horizontal, how much torque would you exert How much torque would you exert when the pedal is vertical Finding Net Torque
Try the following experiment Get two pencils, some coins, and some transparent tape Tape two identical coins to the ends of the pencil and balance it on the second pencil, as shown in Figure 85 Each coin exerts a torque that is equal to its weight, Fg, times the distance, r, from the balance point to the center of the coin, as follows: Fgr But the torques are equal and opposite in direction Thus, the net torque is zero: or Fg1 r1 Fg2 r2 0
How can you make the pencil rotate You could add a second coin on top of one of the two coins, thereby making the two forces different You also could slide the balance point toward one end or the other of the pencil, thereby making the two distances different Figure 85 The torque exerted by the first coin, Fg1r1, is equal and opposite in direction to the torque exerted by the second coin, Fg2r2, when the pencil is balanced Section 82 Rotational Dynamics
Balancing Torques Kariann (56 kg) and Aysha (43 kg) want to balance on a 175mlong seesaw Where should they place the pivot point Analyze and Sketch the Problem
Sketch the situation Draw and label the vectors Known: mK 56 kg mA 43 kg rK rA 175 m
rK rA
Unknown: rK rA
Solve for the Unknown
Find the two forces Kariann: FgK mKg (56 kg)(980 m/s2) 55 102 N Aysha: FgA mAg (43 kg)(980 m/s2) 42 102 N

