chapter 11 Flashcards
what is a collision ?
A collision is a short-duration interaction between two objects. The collision between a tennis ball and a racket, or a baseball and a bat, may seem instantaneous to your eye, but that is a limitation of your perception. A high-speed photograph reveals that the side of the ball is significantly flattened during the collision. It takes time to compress the ball, and more time for the ball to re-expand as it leaves the racket or bat.
the duration of the collision depends on what ?
The duration of a collision depends on the materials from which the objects are made
The harder the objects, the shorter the contact time.
how do you model a colliding ball ?
hows an object colliding with a wall. The object approaches with an initial horizontal velocity vix experiences a force of duration Δt and leaves with final velocity vfx Notice that the object, as in the photo above, deforms during the collision. A particle cannot be deformed, so we cannot model colliding objects as particles. Instead, we model a colliding object as an elastic object that compresses and then expands, much like a spring. Indeed, that’s exactly what happens during a collision at the microscopic level: Molecular bonds compress, store elastic potential energy, then transform some or all of that potential energy back into the kinetic energy of the rebounding object.
what is an impulsive force ?
The force of a collision is usually very large in comparison to other forces exerted on the object. A large force exerted for a small interval of time is called an impulsive force. The graph of Figure 11.1 shows how a typical impulsive force behaves, rapidly growing to a maximum at the instant of maximum compression, then decreasing back to zero.
what is momentum ?
The product of a particle’s mass and velocity is called the momentum of the particle:
(11.3)
momentum= p ≡ mv
is momentum a vector or scalar ?
and what its units ?
Momentum, like velocity, is a vector. The units of momentum are kg m/s.
can you decompose the momomentum ?
The momentum vector p⃗ is parallel to the velocity vector v.→ Figure 11.2 shows that p⃗ , like any vector, can be decomposed into x- and y-components. Equation 11.3, which is a vector equation, is a shorthand way to write the simultaneous equations
px=mvx
py=mvy
One of the most common errors in momentum problems is a failure to use the appropriate signs. The momentum component px has the same sign as vx. Momentum is negative for a particle moving to the left (on the x-axis) or down (on the y-axis).
when does a object have a large momemtum ?
An object can have a large momentum by having either a small mass but a large velocity or a small velocity but a large mass. For example, a 5.5 kg (12 lb) bowling ball rolling at a modest 2 m/s has momentum of magnitude p=(5.5kg)(2 m/s)=11kg m/s. This is almost exactly the same momentum as a 9 g bullet fired from a high-speed rifle at 1200 m/s.
what is impulse ?
Strictly speaking, impulse has units of Ns but you should be able to show that Ns are equivalent to kg m/s, the units of momentum.
jx = impulse
is the area under the curve
what is momentum principle ?
This result, called the momentum principle, says that an impulse delivered to an object causes the object’s momentum to change. The momentum pfx “after” an interaction, such as a collision or an explosion, is equal to the momentum pix “before” the interaction plus the impulse that arises from the interaction:
(11.9)
pfx=pix+Jx
pix+ area under the force curve (force vs time graph)
final velocity for momemtum
which formula ?
the final velocity is vfx=pfx/m.
conservation of momentum ?
the momentum before the collision is the same as the momentum after the collision.
it remains constant in an isolated system.
ex: when a car hits a another car with the same mass (bit was immobile)
the momentum is the same.
this is true in an isolated system where the fnet is equal to 0 .
newtons third law and collisions
you can use newtons third law to describe whats happening during the collision
when the ball hits the when, the ball exerts a force on a ball
in addition, the wall also exerts a force on the ball.
these are equal forces.
so, when the ball loses momentum, the wall will gain an equal amount of that momentum.
choosing a system
be careful when choosing a system.
in order to do a conserve momentum, there must be no forces in your system. Isolated
or else you cant use that;
what a perfectly inelastic collisions ?
and give an example
A collision in which the two objects stick together and move with a common final velocity is called a perfectly inelastic collision.
The clay hitting the floor and the bullet embedding itself in the wood are examples of perfectly inelastic collisions. Other examples include railroad cars coupling together upon impact and darts hitting a dart board.
whats the key to analyzing a perfectly inelastic collisions ?
the key to analyzing a perfectly inelastic collision is the fact that the two objects have a common final velocity.
is a perfectly inelastic collision an isolated system or no ?
A system consisting of the two colliding objects is isolated, so its total momentum is conserved. However, mechanical energy is not conserved because some of the initial kinetic energy is transformed into thermal energy during the collision.
in a inelastic collision , what happens to the energy ?
In an inelastic collision, some of the mechanical energy is dissipated inside the objects as thermal energy and not all of the kinetic energy is recovered.
whats a perfectly elastic collision ?
We’re now interested in “perfect bounce” collisions in which kinetic energy is stored as elastic potential energy in compressed molecular bonds, and then all of the stored energy is transformed back into the post-collision kinetic energy of the objects. A collision in which mechanical energy is conserved is called a perfectly elastic collision.
A perfectly elastic collision is an idealization, like a frictionless surface, but collisions between two very hard objects, such as two billiard balls or two steel balls, come close to being perfectly elastic.
the collision in a perfectly elastic collision must follow 2 laws :
which one ?
The collision must obey two conservation laws: conservation of momentum (obeyed in any collision) and conservation of mechanical energy (because the collision is perfectly elastic). Although the energy is transformed into potential energy during the collision, the mechanical energy before and after the collision is purely kinetic energy.
are perfectly elastic and inelastic collisions happens in real life ?
No collision is perfectly elastic, although collisions between two very hard objects (metal spheres) or between two springs (such as a collision on an air track) come close. Collisions can be perfectly inelastic, although many real-world inelastic collisions exhibit a small residual bounce. Thus perfectly elastic and perfectly inelastic collisions are models of collisions in which we simplify reality in order to gain understanding without getting bogged down in the messy details of real collisions.
what is an explosion ?
An explosion, where the particles of the system move apart from each other after a brief, intense interaction, is the opposite of a collision. The explosive forces, which could be from an expanding spring or from expanding hot gases, are internal forces. If the system is isolated, its total momentum during the explosion will be conserved.
momentum definition in words
Momentum can be defined as “mass in motion.” All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity.
an object with momentum is hard to stop ? why ?
and how do you stop it ?
Any object with momentum is going to be hard to stop. To stop such an object, it is necessary to apply a force against its motion for a given period of time. The more momentum that an object has, the harder that it is to stop. Thus, it would require a greater amount of force or a longer amount of time or both to bring such an object to a halt. As the force acts upon the object for a given amount of time, the object’s velocity is changed; and hence, the object’s momentum is changed.
