6.1:
First Law: Particles in One-dimensional Equilibrium
Newton's first law of motion states that if the sum of all the forces acting on an object is zero, it remains unaccelerated. As a result, the object attains equilibrium.
A car moving at a constant velocity is in equilibrium as the net external force acting on it is zero. To identify forces on an object, construct a free-body diagram, considering the object as a particle.
If the force is applied only in one direction, the object is said to be in one-dimensional equilibrium.
Consider a mass hanging through a massless string from the ceiling. The forces acting on the mass are in the vertical direction. Tension in the string acts in the positive y-direction, while its weight acts in the negative y-direction.
Since the mass is at rest, the net magnitude of force acting on it should be zero.
6.1:
First Law: Particles in One-dimensional Equilibrium
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we spray the surface with talcum powder to make the surface smoother, the object slides farther. If we make the surface even smoother by applying oil on it, the object slides even farther. Extrapolating to a frictionless surface and ignoring air resistance, the object would slide in a straight line indefinitely. Friction thus causes the object to slow down.
Newton’s first law tells us about the equilibrium of a system, which is the state in which the forces on the system are balanced. To create equilibrium, we require a balancing force that will produce a net force of zero. This force must be equal in magnitude but opposite in direction to the resultant force. For example, when a car is parked, all forces on the car must be balanced; the vector sum is 0 N, thus, the net force is zero, and Newton's first law applies. When a car is moving at constant velocity down the street, the net force must also be zero, according to Newton's first law. The car's frictional force between the road and tires opposes the drag force on the car with the same magnitude, producing a net force of zero. A net force of zero does not imply that the car is not moving; instead, it means that the car is not accelerating.
Newton's laws of motion are used in solving problems of mechanics. The basics of problem-solving requires emphasis on specific strategies that are useful in applying Newton's laws of motion. If the problem is one-dimensional—that is, if all forces are parallel—then the forces can be handled algebraically. To solve a problem, we can make a sketch of the situation, using arrows to represent all forces, and then apply Newton's laws to solve the problem.
This text is adapted from Openstax, University Physics Volume 1, Section 5.2: Newton's First Law.