7. A 210-g meter stick is nailed to a wall at its 30-cm mark. The meter stick is

Question

7. A 210-g meter stick is nailed to a wall at its 30-cm mark. The meter stick is free to rotate about this nail (it is not nailed tightly!). Three forces of magnitudes F1 = 5.3 N, F2 = 7.5 N and F3 = 12 N act as shown in the figure, with ?2 = 35? and ?3 = 79?. Let the positive direction of rotation for torques be CW. Find (a) the moment arm for the force F1. (b) the moment arm for the force F2. (c) the moment arm for the force F3. (d) the torque exerted by F1 about the axis of rotation. (e) the torque exerted by F2. (f) the torque exerted by F3. (g) What is the torque exerted by the meter stick

7. A 210-g meter stick is nailed to a wall at its 30-cm mark. The meter stick is free to rotate about this nail (it is not nailed tightly!). Three forces of magnitudes F1 = 5.3 N, F2 = 7.5 N and F3 = 12 N act as shown in the figure, with ?2 = 35? and ?3 = 79?. Let the positive direction of rotation for torques be CW. Find (a) the moment arm for the force F1. (b) the moment arm for the force F2. (c) the moment arm for the force F3. (d) the torque exerted by F1 about the axis of rotation. (e) the torque exerted by F2. (f) the torque exerted by F3. (g) What is the torque exerted by the meter stick?s weight? (h) What is the net torque exerted on the meter stick? (i) Which way would the meter stick start rotating from rest as a result of these torques?

Explanation / Answer

a) l1 = 20cm = 0.2 m

b) l2 = (50-30)*sin35 = 11.47 cm = 0.1147 m

c) l3 = (80-30)*sin79 = 49.08 cm = 0.4908 m

d) T1 = +F1*l1 = 1.06 Nm

e) T2 = -F2*l2 = -7.5*0.1147 = -0.86025 Nm

f) T3 = +F3*l3 = +12*0.4908 = 5.8896 Nm

g) Tnet = T1 + T2 + T3 = +6.08935 Nm

i) counter clock wise

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