Consider the following scenario two equally massed
Double inclined plane – intro to physics
The American Astronomical Society (AAS), based in Washington, DC, was founded in 1899 and is the largest professional astronomy organization in North America. Its roughly 7,000 members include physicists, mathematicians, geologists, engineers, and others with scientific and educational interests in the wide range of topics that make up contemporary astronomy. The American Astronomical Society’s mission is to advance and disseminate humanity’s scientific understanding of the cosmos. Short-duration gamma-ray bursts are thought to be created by neutron star mergers (binary neutron stars and neutron star–black holes) (GRBs). They are also thought to be the primary source of gravitational waves observed by advanced LIGO and advanced VIRGO, as well as the primary source of the universe’s strong r-process components. Whether or not these mergers result in short-duration GRBs is highly dependent on the fate of the remnant’s nucleus (whether, and how quickly, it forms a black hole). To evaluate the fate of the cores of neutron star mergers, we combine the results of Newtonian merger calculations and equation of state studies in this paper. We may assess the distribution of these fates to compare to observations using population studies. Only for equations of state that predict maximum non-rotating neutron star masses below 2.3–2.4 solar masses can black hole cores shape quickly. If GRBs need rapid black hole formation, LIGO/Virgo observed rates compared to GRB rates could be used to constrain the equation of state for dense nuclear matter.
Double inclined plane #12
Internal kinetic energy is conserved in an elastic collision, as we’ve seen. An inelastic collision happens when the internal kinetic energy of the material shifts (it is not conserved). Since there is no conservation of kinetic energy between colliding objects, the forces between them which remove or add internal kinetic energy. Internal forces have the ability to modify the sources of energy within a structure. Internal work can convert some internal kinetic energy into heat transfer in inelastic collisions, such as when colliding objects stick together. Or, as when exploding bolts separate a satellite from its launch vehicle, it can convert stored energy into internal kinetic energy.
An inelastic collision is depicted in Figure 1. Two objects of equal mass approach each other at the same speed and then stick together. [latex]frac12mv2+frac12mv2=mv2[/latex] Their total internal kinetic energy is initially [latex]frac12mv2+frac12mv2=mv2[/latex]. After holding together and conserving momentum, the two artifacts come to a stop. However, after the collision, the internal kinetic energy is zero. Since it decreases internal kinetic energy more than any other form of inelastic collision, a collision in which the objects stay together is often referred to as a perfectly inelastic collision. In fact, such a collision decreases internal kinetic energy to the absolute minimum possible while maintaining momentum.
Inclined plane & pulley physics problems – rotational inertia
Collisions that are elastic and inelastic
A block of mass m = 5.8 kg is pulled up a θ = 25° incline as in
When two things collide, they may either stay together or bounce off each other and remain separate. We’ll go over these two types of collisions in this section, first in one dimension and then in two dimensions.
The particles in an elastic collision detach after impact and retain all of their kinetic energy. Kinetic energy is the energy of motion, and it is discussed in greater depth elsewhere. The law of conservation of momentum comes in handy here, and it can be applied if a system’s net external force is zero. Figure 8.6 depicts a momentum-conserving elastic collision.
Only subatomic particles can collide with perfect elasticity. There are no daily visible examples of perfectly elastic collisions since some kinetic energy is still lost due to frictional heat transfer. Collisions between everyday objects, on the other hand, are almost completely elastic when they occur with nearly frictionless objects and surfaces, such as two steel blocks on ice.
Physics – pully on an incline (2 of 2) with friction
I used to get annoyed by Atwood’s computer. It can be perplexing. However, I’ve discovered that having a detailed understanding of forces and acceleration is required to solve all of the problems that can arise from thinking about this seemingly simple method. So, in the hopes of assisting you, I offer my best understanding.
In the animation on the right, Atwood’s computer is portrayed. It couldn’t be any better. It’s just a pulley with a string or rope tied to two masses running through it. We usually simplify things by assuming that the string/rope and the pulley wheel have negligible mass.
The number of forces pulling on either end of a loop, rope, wire, cable, and so on is known as stress. When forces pull in opposite directions, they are additive. The force at one end of a moving string in certain problems is not a pulling force, but rather acts in the opposite direction. It must be subtracted from the force pulling from the opposite end in this situation. (A string under stress is one that has two “pushing” forces.)
Note: We typically make two simplifications in the simplest of Atwood’s machine problems: the mass of the pulley is zero, and the pulley/rope mechanism is frictionless. We’ll be able to loosen those constraints once we’ve mastered the basic problems.