Statics Equilibrium problem

In summary, a statics equilibrium problem involves analyzing the forces acting on a stationary object or system to determine if it is balanced. The steps to solve such a problem include drawing a free body diagram, identifying forces, applying equations of static equilibrium, and checking the solution. Common types of statics equilibrium problems include finding tension, calculating normal force, and solving for weight. Forces are measured in newtons or pounds and distances in meters or feet. Answers can be checked by ensuring net force and torque are zero, comparing to a known value, or using common sense.
  • #1
2
0
Question:

Three forces of magnitude 45 kN, 24 kN and 12 kN are applied to the truss connection as shown. Knowing that the connection is in equilibrium, determine the magnitude of the forces C and T.

fI9E29j.jpg

Equations:

Fx = 0
Fy = 0

My attempt:

Fx=0:

-24kN + Tcos40 + Csin20 = 0

Fy = 0:

45kN + Tsin40 - Ccos20 = 0

By substitution:

Divide first equation by sin20:

2.24T + C = 70.17 kN ---> C = 70.17kN - 2.24T (Plug that C into equation 2.)

Tsin40 - (70.17kN - 2.24T)(cos20) = -45kN

2.75T = 20.94

T = 7.62kN (Plug that back into equation 1 to find C)

C = 53.10 kN

However the answer is supposed to be C = 44.89kN and T = 4.35kN

What am I doing wrong?
 
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  • #2
How do you get your Fx equation?
 
  • #3
For a start sign convention:
∧ +ve & >+ve

v=0
-24 + CCos70 = TCos40 +12​
h=0
-CSin70 = TSin40 +45

from here you should be able to get answer​
 
  • #4
I think you missed the 12 kN in your Fx equation. I didn't go through the math though.
 

What is a statics equilibrium problem?

A statics equilibrium problem is a type of physics problem that involves analyzing the forces acting on a stationary object or system in order to determine whether it is in equilibrium or balanced. In other words, the net force and net torque acting on the object must be equal to zero for it to be in static equilibrium.

What are the steps to solve a statics equilibrium problem?

The steps to solve a statics equilibrium problem include:

  1. Draw a free body diagram of the object or system
  2. Identify all the forces acting on the object and their respective magnitudes and directions
  3. Apply the equations of static equilibrium (ΣF = 0 and Στ = 0) to the object
  4. Solve for any unknown forces or distances
  5. Check your answer by ensuring that the net force and net torque are equal to zero

What are some common types of statics equilibrium problems?

Some common types of statics equilibrium problems include:

  • Finding the tension in ropes or cables supporting an object
  • Calculating the normal force on an object resting on a surface
  • Determining the force required to keep an object in equilibrium on an incline
  • Analyzing the forces acting on a seesaw or lever system
  • Solving for the weight of an object using a pulley system

What are the units of measurement for forces and distances in statics equilibrium problems?

Forces are typically measured in units of newtons (N) or pounds (lb), while distances are measured in meters (m) or feet (ft). It is important to ensure that all forces and distances are in the same units when solving a statics equilibrium problem to avoid errors in calculations.

How can I check my answer to a statics equilibrium problem?

You can check your answer by making sure that the net force and net torque on the object are equal to zero. If they are not equal to zero, then there is an error in your calculations. You can also check your answer by comparing it to a known value or using common sense to determine if the solution is reasonable.

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