Regardless of their mass all objects fall to Earth's surface at the same rate. Why does the downward acceleration of gravity not depend on mass?
Just how much water does a large ship need to float? Could, for example, a battleship float in a bathtub? Panama Canal locks provide a good illustration.
The reason drafting, or riding behind another rider, is common in bicycle but not running races results from the physics of air resistance.
How friction from tidal forces affects the Earth and Moon, slowed the Moon's rotation rate until a lunar day equals a month, and slows Earth's rotation.
A scientific look at the urban myth that tidal forces on amniotic fluid cause more babies to be born during the full Moon.
Ocean tides result from tidal forces caused by the difference in gravitational forces from the Moon and Sun at differing locations on Earth.
Momentum is the mass times the velocity. In the absence of external forces, the total momentum of an isolated system must be conserved and remain constant.
Conservation laws are very important in physics. Certain fundamental quantities including momentum, angular momentum, energy, mass, and charge are conserved. The total amount of these conserved quantities must remain constant and can neither increase nor decrease.
These conservation laws are very powerful problem solving tools in physics. Because the conserved quantity remains constant regardless of various other conditions in the system, information about these quantities is not needed to solve the problem.
What is Momentum
Momentum, p, is defined as the mass, m, multiplied by the velocity, v. In equation form this law is expressed as:
p = mv
Both momentum and velocity are vector quantities as expressed by the boldface symbols. The direction matters. When adding momenta, just as when adding velocities, the rules for vector addition must be used. When solving two or three dimensional momentum problems, it is also absolutely essential to divide the momentum into x, y, and z components.
Law of Conservation of Momentum
The law of conservation of momentum applies only to isolated systems that have no external forces acting on the system. It states that if a system has no external forces acting on it, then the total momentum of the system must be conserved. The momentum of this system stays the same and can neither increase nor decrease.
There are no known exceptions to this law!
When there is an external force, the force multiplied by the time over which the force acts is defined as the impulse and equals the change in momentum.
Examples of Momentum Conservation
Imagine a sailboat that can't get where it's going because there is no wind. Now if the captain sets up a huge fan on the boat to blow wind into the sails, would the sailboat move? A large enough fan that is not on the boat could blow the boat, but if the fan were on the boat the boat would not go anywhere. The fan and boat constitute a closed system, so the total momentum can not change. It stays zero.
The recoil from a gun and rocket propulsion are also examples of conservation of momentum. The initial momentum is zero. The bullet or rocket fuel have momentum in one direction. To keep the total momentum zero, the rocket and gun have the same momentum in the opposite direction.
Homework Problem Solving Help
To solve conservation of momentum homework problems analyze the situation, with the help of appropriate diagrams, of the initial and final states. Find the total momentum in each state and set them equal. If the problem is two or three dimensional, then the various momenta involved in the problem must be divided into x, y, and possibly z coordinates. Momenta cannot be added without doing this step. Solve for the unknown quantities in the equations.
Collision Problems
One frequent application of momentum conservation is for collision problems in physics. When two objects collide they act as an isolated system. Hence the total momentum before the collision equals the total momentum after the collision.
In cases where there are external forces, such as gravity, acting on the system physicists make the fairly accurate approximation that the collision occurred rapidly enough that the external forces do not have enough time to affect the collision.
The law of conservation of momentum is a fundamental physical principle with no known exceptions and considerable problem solving power.
Further Reading
Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.
Copyright Paul A. Heckert