Torque about a pendulum's suspension point

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SUMMARY

The discussion focuses on calculating the torque about a pendulum's suspension point due to the weight of the bob. The user initially applied the torque formula τ = rFsin(θ) with incorrect assumptions, leading to a calculated torque of 1.7 Nm instead of the correct value of 2.0 Nm. The correct approach involves using τ = lF, where l is the effective length of the pendulum, which was determined to be 0.80 m. The gravitational force (F_g) acting on the bob is calculated using F_g = mg, with m = 0.50 kg and g = 9.8 m/s².

PREREQUISITES
  • Understanding of torque and its calculation using τ = rFsin(θ)
  • Knowledge of gravitational force calculation using F_g = mg
  • Familiarity with trigonometric functions, specifically sine
  • Basic principles of pendulum mechanics
NEXT STEPS
  • Study the derivation and application of the torque formula τ = lF
  • Learn about the effects of angle on torque calculations in pendulum systems
  • Explore the relationship between mass, gravity, and torque in rotational dynamics
  • Investigate common mistakes in torque calculations and how to avoid them
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators looking for examples of torque calculations in pendulum systems.

JessicaHelena
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Homework Statement


In the figure attached, what is the torque about the pendulum's suspension point produced by the weight of the bob, given that the mass is 40 cm to the right of the suspension point, measured horizontally, and m=0.50kg?

Homework Equations


tau = rFsin (theta)
or
tau = lF

The Attempt at a Solution


I don't know why but I tend to prefer the first equation, so upon seeing this, I thought the F_g = mg is pulling down on the suspension point at an angle of 60°, so I can do tau = L*m*g*sin(60°).
From the given information about the 40cm, we can draw a right triangle and get that L = 0.80m.
sin 60° is sqrt(3)/2.
m = 0.5 kg
g is a constant 9.8.
Then multipling them all together, I got 1.7Nm.

However, apparently I am wrong — it should be 2.0 Nm, and no, it isn't a matter of rounding 1.7Nm up to 2.0Nm. The solution provides a way of using the second equation, but I'd like to know why I was wrong using the 1st equation. Could someone help me out?
 

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JessicaHelena said:
I don't know why but I tend to prefer the first equation
Good (or perhaps not good...) ! But what is ##\theta## ? and F ?

Template said:
all variables and given/known data
A picture showing F and ##\theta## would really help
 
JessicaHelena said:
an angle of 60°, so I can do tau = L*m*g*sin(60°).
Think that through again.
 

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