Question

Differentiate between translational equilibrium and mechanical equilibrium​

Answer 1

Answer:

We say an object is in translational equilibrium when the sum of all the external forces acting on the object equals zero. Since a force is a mass times an acceleration, another way to look at this is that an object is in translational equilibrium when it is experiencing zero overall acceleration. This can mean either the object is not moving, or it is moving at a constant velocity.

If we can tell that an object is in translational equilibrium, we can use this to help find all the forces affecting that object. Imagine trying to push a 20-kilogram box along the floor. You push with an applied force of 200 Newtons, but the box doesn't budge an inch. Since our box isn't moving, it must be in translational equilibrium. Using the info given, let's find all the forces acting on the box.

In this example, there are actually four forces acting on the box: an applied force from you, a frictional force stopping you from moving the box, the force due to gravity pushing down, and the normal force from the floor pushing up on the box. The first thing we do is use our box's mass and the acceleration due to gravity to find the force due to gravity.

force due to gravity equation

force due to gravity partially solved

force due to gravity solution

Now we just need to find the normal and frictional forces. To do this we are going to create two separate equations. In 2D we can split our forces up into those acting in the x direction (horizontally) and those acting in the y direction (vertically). The sum of the horizontal forces alone, and the sum of the vertical forces alone, both must equal zero since the box is in translational equilibrium.

horizontal forces sum

vertical forces sum

Our force applied and the frictional force are the horizontal forces. The force due to gravity and the normal force are the vertical forces. With this we can find both our unknown forces. We'll start with finding the frictional force.

finding frictional force part 1

finding frictional force part 2

finding frictional force solution

Next, we'll find the normal force.

finding normal force part 1

finding normal force part 2

finding normal force solution

The negative signs make sense because they show that the force due to gravity and the frictional force are acting in opposite directions from the normal force and applied force respectively.

Answer 2

Answer:

An object is in translational equilibrium when the sum of all the external forces acting on the object equals zero. ... In rotational equilibrium, an object either will not be moving or moving at a constant angular velocity. This must mean the object is experiencing zero angular acceleration

Explanation:

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