What mass must be placed on the cord to keep the pulley from rotating?

Click For Summary
SUMMARY

The discussion centers on determining the mass required to prevent a pulley from rotating, specifically calculating that mass as 2.5 kg. The net torque must equal zero, leading to the equation ## F_{r}r - Mgr = 0 ##, where ## F_{r} ## is the force exerted by a 5 kg mass on a ramp and ## F_{d} ## is the downward force from the other mass. The analysis reveals potential confusion regarding the different radii of the pulley, indicating that the two cables may operate on separate wheels within the same pulley system.

PREREQUISITES
  • Understanding of torque and its calculation in rotational systems
  • Familiarity with basic physics concepts such as force and mass
  • Knowledge of pulley systems and their mechanics
  • Ability to interpret and manipulate equations involving trigonometric functions
NEXT STEPS
  • Study the principles of rotational dynamics and torque calculations
  • Learn about the mechanics of pulley systems and their applications
  • Explore the implications of different radii in pulley systems
  • Investigate the effects of friction and mass distribution on pulley performance
USEFUL FOR

Students studying physics, engineers working with mechanical systems, and anyone interested in understanding the dynamics of pulleys and rotational motion.

I_Try_Math
Messages
119
Reaction score
25
Homework Statement
What hanging mass must be placed on the cord to keep the pulley from rotating (see the following figure)? The mass on the frictionless plane is 5.0 kg. The inner radius of the pulley is 20 cm and the outer radius is 30 cm.
Relevant Equations
## \tau = rFsin\theta ##
I suppose to keep the pulley from rotating the net torque has to be zero?
Let ## F_{r} ## be the force that the 5 kg mass on the ramp exerts on the pulley and ## F_{d} ## be the force exerted straight down by the other mass on the pulley.
Let ## r = 0.3 ## m be the outer radius of the pulley.
## \sum \tau_{i} = F_{r}rsin90 - F_{d}rsin90 = 0 ##
## F_{r}r - Mgr = 0 ##
## r5gsin30 - rMg = 0 ##
## \Rightarrow M = 2.5 kg ##

I'm wondering if I solved for ##F_{r} ## incorrectly? Or there's some other mistake? Any hints are appreciated.
 

Attachments

  • 7-16-q-75.png
    7-16-q-75.png
    13.4 KB · Views: 91
Physics news on Phys.org
It is very unclear, but it looks to me that the two cables are at different distances from the centre of the pulley. This suggests that the two radii given refer to two different wheels side by side on the same pulley. The drawing shows a dark inner annulus and lighter grey outer annulus.
 
  • Like
Likes   Reactions: I_Try_Math

Similar threads

Replies
15
Views
2K
  • · Replies 30 ·
2
Replies
30
Views
4K
  • · Replies 40 ·
2
Replies
40
Views
5K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 28 ·
Replies
28
Views
6K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 21 ·
Replies
21
Views
1K
  • · Replies 6 ·
Replies
6
Views
938