Mass Pulley System, Acceleration

Click For Summary
SUMMARY

The discussion focuses on calculating the acceleration of a mass pulley system involving a 1 kg block on a 20° incline and a 2 kg hanging block, with a friction coefficient of μk=0.45 and a frictionless pulley of mass 0.10 kg. The relevant equations include Newton's second law (ΣF=ma), rotational motion (ΣF=Iα), and the friction equation (ƒk=μN). The user initially struggled with incorporating the radius of the pulley into the tension equations but successfully resolved the issue by recognizing the need for the radius in the equation (T2-T1)=Iα. The final solution incorporates all necessary variables and calculations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of frictional forces and their calculations
  • Ability to draw and interpret free body diagrams
NEXT STEPS
  • Study the concept of moment of inertia for different shapes, particularly disks
  • Learn how to derive equations of motion for systems involving pulleys
  • Explore advanced applications of Newton's laws in multi-body systems
  • Investigate the effects of varying coefficients of friction on acceleration
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the dynamics of pulley systems and inclined planes.

ryankunzzz
Messages
21
Reaction score
0

Homework Statement


A block of 1kg is resting on an incline of 20° that has a coefficient of friction μk=0.45 with the surface. It is connected with a mass less string to a friction-less pulley of mass 0.10 kg to a hanging block of 2 kg. What is the acceleration of the system without ignoring rotational inertia. Model the pulley as a disk.

Homework Equations



First we need Newtons 2nd law, ΣF=ma
Also for rotational motion ΣF=Iα
and friction is ƒk=μN where N is the normal force.

The Attempt at a Solution


[/B]
After drawing my free body diagrams, I was left with this :

But I'm stumped there, I feel like I'm missing something obvious.

I want to plug the two equations for the tensions into the pulley equation, but then I'm still missing the radius of the pulley.

pDYs1xT.jpg

EDIT: The -m2g in the last equation on the right should be m2a

EDIT #2: I forgot the R on the (T2-T1)=IAlpha, I solved it. Thanks.
 
Last edited:
Physics news on Phys.org
Well done ... and good work doing all the algebra before subbing in the values.
 

Similar threads

Analyzing acceleration of block on a ramp connected to a pulley
  • · Replies 15 ·
Replies
15
Views
2K
Newton's Second Law (Pulley Sustem)
  • · Replies 3 ·
Replies
3
Views
2K
Ideal Vs Real Mass Pulley system
  • · Replies 10 ·
Replies
10
Views
5K
Accelerating pulleys (3 pulleys and 3 masses)
  • · Replies 5 ·
Replies
5
Views
2K
Pulley system problem: 6 Pulleys and 1 Mass
  • · Replies 5 ·
Replies
5
Views
1K
Olympiad dynamics problem with 3 masses and a pulley
  • · Replies 17 ·
Replies
17
Views
3K
Two blocks, a fixed pulley and friction
  • · Replies 4 ·
Replies
4
Views
3K
Block-pulley system and rotational dynamics
  • · Replies 5 ·
Replies
5
Views
5K
System of two pulleys and three masses
  • · Replies 22 ·
Replies
22
Views
6K
Angular Acceleration and Linear Acceleration of a Pulley
  • · Replies 4 ·
Replies
4
Views
2K