Mechanical Equilibrium

How can you express the equilibrium rule mathematically?

ΣF=0

How can you change an object's state of motion?

A force is needed to change an object's state motion

How are dynamic and static equilibrium different?

Objects at rest are said to be in static equilibrium; Objects moving ata constant speed in a straight line path are said to be in dynamic equilibrium.

Consider two forces, one having a magnitude of 20 N and the other a magnitude of 12 N. What is the maximum net force possible for these two forces? The minimum?

The maximum net force for these two forces is 32 N. This would be possible if the forces are going in the same direction, as force is a vector quantity. The minimum force would be 8, if the forces were going in opposite directions and you had to subtract.

Two children push on a crate. They find that when they push together horizontally with forces of 155 N and 187 N, respectively, the crate slides across the floor at a constant speed. Show that the force of friction of the crate and the floor is 342 N.

155 N + 187 N = 342 N. If the crate is moving along the floor at a constant velocity, it's in dynamic equilibrium. Since ΣF=0 in equilibrium, the friction counters the force of the push, making it 342 N.

Can an object be moving and still be in equilibrium?

An object can be in equilibrium and in motion because of dynamic equilibrium. An object is defined as having equilibrium when the total net forces acting on it are zero. As long as there is an equal force to counter the force of the motion, the object is stated to be in equilibrium. This would translate to the object moving in a straight line at a constant speed. The object would be moving and still in equilibrium.

For an object to rest on a horizontal surface, what is the support force equal to?

For the object at rest on a horizontal surface, the support force must equal the object's weight.

A cat lies on the floor. Can you say that no force acts on the cat? Or is it correct to say that no net force acts on the cat? Explain.

If the cat is static, then it is in equilibrium. The definition of equilibrium is that the net force on an object is zero. Although the force of gravity is pulling the cat down, the support force of the floor counteracts it. Therefore, no net force acts on the cat.

How can you find the resultant of two vectors?

To find the resultant of two vectors, construct a parallelogram wherein the two vectors are adjacent sides. The diagonal of the parallelogram shows the resultant.