For this problem, we are looking at the net force on the bone. Since both dogs are pulling with the same force, we can say the magnitude of the force of dog 1 equals the magnitude of the force of dog 2, but in opposite directions. Mathematically, \(\displaystyle F_1=-F_2\).

To find the net force on the bone, we add the individual forces together.

\(\displaystyle F_{net}=F_1+F_2\)

We can substitute our forces into the equation for net force.

\(\displaystyle F_{net}=(-F_2)+F_2\)

\(\displaystyle F_{net}=0N\)

The net force is zero. Each dog pulls with equal force in opposite directions, allowing the total force to cancel out.

According to Newton's second law, \(\displaystyle F_{net}=ma\). If the net force is zero, then the acceleration of the bone must also be zero.

\(\displaystyle 0N=ma\)

\(\displaystyle a=0\frac{m}{s^2}\)

If the drop is at rest, then that means that the net forces acting upon it are equal to zero. There are two forces acting on the drop: the force due to gravity and the frictional force of the paint on the wall.

Mathematically, we can set up an equation for the net force:

\(\displaystyle F_{net}=F_f-F_G\)

\(\displaystyle 0=F_f-F_G\)

\(\displaystyle -F_G=F_f\)

The forces of friction and gravity are going to be equal and opposite, causing the drop to remain still on the wall.

If two forces act on a single object, then the net force on the object is equal to the sum of the forces acting on it.

\(\displaystyle F_{net}=F_1+F_2+...\)

Forces are vector quantities, however. This means that all forces have a magnitude and a direction of action. When adding forces, we must take their directions into account. Directions are broken into horizontal and vertical portions for vector addition, and can be positive or negative based on the direction along the axis.

For a net force to be zero, one force must be positive and the other must be negative along a given axis. If the forces are of equal magnitude, then they must be acting in exactly opposite directions in order to cancel each other.

\(\displaystyle F_1=-F_2\)

\(\displaystyle F_{net}=F_1+F_2=(-F_2)+F_2=0\)

Kinetic force is not a technically correct property. Kinetic energy can be used to generate force, but is not a force in itself. Forces require non-zero acceleration, meaning that they only exist when there is a changein velocity. A change in kinetic energy can indicate a change in velocity, leading to a non-zero force value.

Normal force is the force of a surface upon an object, frequently countering gravity. Friction force is the resistance between an object and a surface, and acts opposite the direction of the object's motion. Buoyant force is the upward force of a fluid on a submerged object. Drag, or air resistance, is a special form of friction force for an object moving through a fluid.