Resultant Of Coplanar Force Systems
Sample Solution
A common example of a force system in daily life is a person standing on a scale.
Different Types of Forces in the Force System
There are two main types of forces in this force system:
- Applied forces: These are forces that are applied to the object by an external agent. In this case, the applied force is the weight of the person.
- Non-applied forces: These are forces that are exerted on the object by its surroundings. In this case, the non-applied force is the normal force exerted by the scale.
Full Answer Section
Real-World Example of an Equivalent Force System
A real-world example where the actual forces on an object or structure can be replaced with an equivalent system of forces is a beam supported by two cables.
Actual Forces on the Beam
The actual forces on the beam are the weight of the beam and the tension in the two cables.
Equivalent Force System
The equivalent force system is a single force acting at the center of mass of the beam. This force is equal to the resultant of the weight of the beam and the tension in the two cables.
Equivalence of the Two Force Systems
The two force systems are equivalent because they produce the same effect on the beam. The beam will be in equilibrium under both force systems.
Analysis of the Beam
The beam can be analyzed using the equivalent force system by applying the following equations:
∑Fx = 0
∑Fy = 0
where:
- ∑Fx is the sum of the forces in the x-direction
- ∑Fy is the sum of the forces in the y-direction
By solving these equations, we can determine the tension in the two cables.
Conclusion
Coplanar force systems are a useful tool for analyzing the forces acting on objects and structures. By representing the forces as vectors, we can use the equations of equilibrium to solve for the unknown forces.
Another Example of a Force System in Daily Life
Another common example of a force system in daily life is a car driving on a road.
Different Types of Forces in the Force System
There are several different types of forces acting on a car driving on a road, including:
- Weight of the car: This is a downward force that is applied by gravity.
- Normal force of the road: This is an upward force that is exerted by the road on the tires of the car.
- Frictional force of the road: This is a force that opposes the motion of the car.
- Force of the engine: This is a forward force that is applied by the engine of the car.
Real-World Example of an Equivalent Force System
One real-world example where the actual forces on an object or structure can be replaced with an equivalent system of forces is a car driving on a straight, level road.
Actual Forces on the Car
The actual forces on the car are the weight of the car, the normal force of the road, the frictional force of the road, and the force of the engine.
Equivalent Force System
The equivalent force system is a single force acting in the direction of travel of the car. This force is equal to the resultant of the weight of the car, the normal force of the road, the frictional force of the road, and the force of the engine.
Equivalence of the Two Force Systems
The two force systems are equivalent because they produce the same effect on the car. The car will be in equilibrium under both force systems.
Analysis of the Car
The car can be analyzed using the equivalent force system by applying the following equations:
∑Fx = 0
∑Fy = 0
where:
- ∑Fx is the sum of the forces in the x-direction
- ∑Fy is the sum of the forces in the y-direction
By solving these equations, we can determine the acceleration of the car.
Conclusion
Coplanar force systems can be used to analyze a wide variety of real-world problems. By understanding the different types of forces that can act on objects and structures, we can use coplanar force systems to solve for unknown forces and accelerations.