Laws of Motion with Static Equilibrium

In summary, the conversation discusses finding the values of θ and W in a figure with given values for w1, w2, and α. The equations used to solve for the unknowns are T_1=25/sin(alpha), F_x=-T_1cos(alpha)+T_2cos(theta), and F_y=T_1sin(alpha)+T_2sin(theta)-2. The tension in the leftmost rope is found to be 16/sin(alpha) due to the vertical component of T_1 being 16. The tension in the piece of the leftmost rope hanging straight down is the same as T_1.
  • #1
Keithkent09
33
0

Homework Statement


Find θ and W in the figure below where w1 = 16.0 N, w2 = 25.0 N, and α = 66.5°, assuming that the arrangement is at rest.

Homework Equations


T_1=25/sin(alpha)
F_x=-T_1cos(alpha)+T_2cos(theta)
F_y=T_1sin(alpha)+T_2sin(theta)-2

The Attempt at a Solution


I tried to use the above equations to solve for the three unknowns. First I found the tension of the string on the left, then plugged that into the second two equations to find the remaining values and I could not get the correct answers.
 

Attachments

  • weights.gif
    weights.gif
    12.6 KB · Views: 701
Physics news on Phys.org
  • #2
Keithkent09 said:
T_1=25/sin(alpha)

Why is this true? What are tensions T1 and T2 in each rope?
 
  • #3
Sorry I meant that it is 16/sin(alpha).
This is because the vertical component of T_1 is 16 because of w_1. So using trig T_1=17.447. I am doing this the correct way and just making some kind of simple mistake?
 
  • #4
A pulley changes the direction of the tension without changing its magnitude. What is the tension in the piece of the leftmost rope that is hanging straight down?
 

Related to Laws of Motion with Static Equilibrium

1. What are the three laws of motion?

The three laws of motion are fundamental principles developed by Sir Isaac Newton to describe the behavior of objects in motion. They are:

  • First Law: An object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity unless acted upon by an external force.
  • Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be written as F=ma, where F is the net force, m is the mass, and a is the acceleration.
  • Third Law: For every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back.

2. How do the laws of motion relate to static equilibrium?

The first law of motion states that an object at rest will remain at rest unless acted upon by an external force. In the case of static equilibrium, the object is not moving, so the net force acting on it must be zero. This means that the forces acting on the object must be balanced, in accordance with the first law of motion.

3. What is the difference between static and dynamic equilibrium?

Static equilibrium occurs when an object is at rest and the forces acting on it are balanced, resulting in a net force of zero. Dynamic equilibrium, on the other hand, occurs when an object is in motion at a constant velocity, and the forces acting on it are balanced, resulting in a net force of zero. In both cases, the object is in a state of equilibrium, but the difference lies in whether the object is at rest or in motion.

4. How do you determine if an object is in static equilibrium?

To determine if an object is in static equilibrium, you must analyze the forces acting on the object. If the object is at rest and the forces are balanced, resulting in a net force of zero, then the object is in static equilibrium. This means that the object will not move or rotate, and all of the forces acting on it are canceled out.

5. Can an object be in both static and dynamic equilibrium simultaneously?

No, an object cannot be in both static and dynamic equilibrium simultaneously. The two states of equilibrium are mutually exclusive, as an object cannot be at rest and in motion at the same time. An object can only be in one state of equilibrium at a time, depending on its motion and the forces acting on it.

Similar threads

Static equilibrium: setting up the equation
    • Introductory Physics Homework Help
Replies
11
Views
2K
What is the Direction of Normal Force in Static Equilibrium on a Ramp?
    • Introductory Physics Homework Help
Replies
5
Views
1K
Spring static equilibrium Problem
    • Introductory Physics Homework Help
2
Replies
57
Views
4K
Find angle for the ring to be in equilibrium
    • Introductory Physics Homework Help
Replies
2
Views
1K
Magnetic Field required to hold a loop in static equilibrium
    • Introductory Physics Homework Help
Replies
5
Views
4K
I Statics: When the reactions depend on the displacements
    • Mechanics
Replies
5
Views
900
Finding Total Charge from E-field
    • Introductory Physics Homework Help
Replies
9
Views
2K
Angles in a Static Equilibrium
    • Introductory Physics Homework Help
Replies
9
Views
2K
Find min/max accel. for block to stay on wedge (static fric)
    • Introductory Physics Homework Help
Replies
1
Views
2K
A simple static equilibrium problem
    • Introductory Physics Homework Help
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top