Torque about a pendulum's suspension point

Click For Summary
The discussion centers on calculating the torque produced by a pendulum's bob weight at a suspension point. The user initially applies the torque formula tau = rFsin(theta) but miscalculates the effective length (L) and the angle (theta). They derive a torque of 1.7 Nm but are informed that the correct value is 2.0 Nm. The conversation highlights the importance of accurately determining the angle and the effective lever arm in torque calculations. Clarification on the variables and correct application of the formulas is sought to understand the discrepancy in the results.
JessicaHelena
Messages
188
Reaction score
3

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?
 

Attachments

  • IMG_0306.jpg
    IMG_0306.jpg
    34.1 KB · Views: 528
Physics news on Phys.org
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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

Similar threads

  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
1
Views
1K
Replies
3
Views
1K
  • · Replies 5 ·
Replies
5
Views
6K
  • · Replies 6 ·
Replies
6
Views
2K