3 Basics of Particles
What is a Particle?
What is a ? The simplest image of a particle is probably just a ball. What properties apply to all particles? We talked about particles a lot in Physics 131 in the point mass approximation, but it’s probably best that we flush out our definitions.
In its most generic sense, a particle is a chunk of stuff. It exists in a particular place and at a particular time and a particle doesn’t go around corners. Particles can, but do not necessarily have to, have mass, we will talk about a massless particle in a later section. But all particles can be thought of as having momentum, that quantity from 131 of mass times velocity. Particles can also be thought of as having energy.
Instructor’s Note
In summary, you need to know that particles can be thought of as balls with defined position and speed and are characterized by:
- Their energy
- Their momentum
- How many of them there are
Linear Momentum and Force (Review from Physics 131)
This material is review from physics 131, but we will use these ideas in this unit, so here is a short refresher.
Instructor’s Note
You quiz will cover:
- Calculate the momentum for any object
- Recall that momentum is a vector
- From the change in momentum, compute the average force
The scientific definition of linear momentum is consistent with most people’s intuitive understanding of momentum: a large, fast-moving object has greater momentum than a smaller, slower object. Linear momentum is defined as the product of a system’s mass multiplied by its velocity. In symbols, linear momentum is expressed as
.
Momentum is directly proportional to the object’s mass and also its velocity. Thus the greater an object’s mass or the greater its velocity, the greater its momentum. Momentum p is a vector having the same direction as the velocity v. The SI unit for momentum is kg⋅m/s.
Example Calculating Momentum: A Football Player and a Football
(a) Calculate the momentum of a 110-kg football player running at 8.00 m/s.
(b) Compare the player’s momentum with the momentum of a hard-thrown 0.410-kg football that has a speed of 25.0 m/s.
Strategy
No information is given regarding direction, and so we can calculate only the magnitude of the momentum, p. In both parts of this example, the magnitude of momentum can be calculated directly from the definition of momentum given in the equation, which becomes
when only magnitudes are considered.
Solution for (a)
To determine the momentum of the player, substitute the known values for the player’s mass and speed into the equation.
Solution for (b)
To determine the momentum of the ball, substitute the known values for the ball’s mass and speed into the equation.
The ratio of the player’s momentum to that of the ball is
Discussion
Although the ball has greater velocity, the player has a much greater mass. Thus the momentum of the player is much greater than the momentum of the football, as you might guess. As a result, the player’s motion is only slightly aff