Pendulum problem - What is the magnitude of the torque?

AI Thread Summary
The discussion centers on calculating the torque of a pendulum with a mass of 0.75 kg attached to a 1.25 m rod at a 30-degree angle from the vertical. The initial calculations yielded a torque of -9.2 N, but the expected answer is half of that value. Participants suggest that the error may stem from misinterpreting the angle or the vector components involved in the torque calculation. A corrected approach involves using the cosine of the angle to resolve the vector magnitude accurately. The final torque calculation, after adjustments, results in 4.6 Nm.
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a small mass of 0.75kg is attached to one end of a 1.25m long massless rod, and the other end is hung from a pivot. When the resulting pendulum is 30degrees from the vertical what is the magnitude of the torque about the pivot?

what i did:
-Fsin30 -mg = 0
Fsin30 = -mg
F = -14.7N

t = rFsin30
t = 1.25(-14.7sin30)
t = -9.2N

the answer is supose to be half of this what did i do wrong?
 
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I always always draw out the problem and figure it out geometrically on paper rather than resort to filling in formuals. Check out the attachment. Its easy to see from this that you need to find the vector mag. that acts on the tangent of the rods arc. Get the angle. Its 60. Get the resolved vector magnitude.

cos 60= F/7.36

Torque = 3.68 x 1.25
=4.6 Nm

Was your diagram maybe screwed up?>?
 

Attachments

Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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