Dynamics of a Box attached to a pully

In summary, the conversation discusses a physics problem involving two bodies on an incline with coefficients of friction and an angle. The acceleration of body A is calculated using unit-vector notation for three different scenarios. The attempt at a solution is shown, with a mistake in the equation due to confusion between mass and weight. The correct solution is then provided.
  • #1
ciubba
65
2

Homework Statement


Body A in Fig. 6-33 weighs 102 N, and body B weighs 32 N. The coefficients of friction between A and the incline are μs 0.56 and μk 0.25. Angle θ is 40. Let the positive direction of an x-axis be up the incline. In unit-vector notation, what is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down
the incline?

Free body diagram: http://postimg.org/image/fh6livrer/

See attached picture (problem 27)
http://postimg.org/image/5svunp27z/

Homework Equations


Fnet=ma

The Attempt at a Solution



Clearly the answer to part a is 0-- I'm stuck on part b.

For B, [tex] F_{Net, y}= -m_B a_y = F_T -m_B g \rightarrow F_T = m_B g - m a_y[/tex]

For A, [tex] F_{Net, x}=ma_x = - \mu _k m_A g cos(40) +F_T - m_A g sin(40)[/tex]

Plugging in the information,

[tex] 102 a= -0.25*102*cos(40)+32-32a -102sin(40) \rightarrow a=-.39[/tex]

However, the book lists the correct answer as -3.9, so I'm off by a power of ten. Where did I go wrong?
 
Physics news on Phys.org
  • #2
Be sure to distinguish between mass and weight.
 
  • #3
D'oh! It should be

[tex]
\frac {102}{9.8} a= -0.25*102*cos(40)+32- \frac {32}{9.8}a -102sin(40) \rightarrow a=-3.82 [/tex]

Thanks!
 
  • #4
Good.
(I get -3.88 m/s2, but close enough).
 

1. What is the dynamics of a box attached to a pulley?

The dynamics of a box attached to a pulley refers to the motion and forces involved when a box is connected to a pulley system. It involves understanding the relationship between the box, the pulley, and the forces acting on them.

2. How does the weight of the box affect the dynamics of the system?

The weight of the box determines the force it exerts on the pulley system and affects the overall dynamics. A heavier box will require more force to lift and will exert a greater force on the pulley system.

3. What is the role of friction in the dynamics of a box attached to a pulley?

Friction plays a crucial role in the dynamics of a box attached to a pulley. It affects the movement of the box and the tension in the rope. Without friction, the box would slide freely and the pulley would not be able to lift it.

4. How does the angle of the rope affect the dynamics of the system?

The angle of the rope affects the direction and magnitude of the force exerted on the box. As the angle increases, the force required to lift the box also increases. It is important to consider the angle when analyzing the dynamics of the system.

5. How can the dynamics of a box attached to a pulley be calculated?

The dynamics of a box attached to a pulley can be calculated using the principles of Newton's Laws of Motion. By considering the forces acting on the box and the pulley, the acceleration and motion of the system can be determined using mathematical equations.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
4K
Back
Top