3B7 Collisions Flashcards
Describe the different kinds of collisions, including the role of conservation of momentum and mechanical energy.
Define:
Collision
Event where two or more objects come into contact with each other, typically with force, causing a change in their motion.
Collisions are analyzed to understand the forces, momentum, and energy exchange between objects.
True or false:
All collisions involve the objects sticking together.
False
In some collisions, objects bounce off each other, while in others, they may stick together. The type of collision affects how energy and momentum are conserved.
Explain the importance of studying collisions.
It helps us understand fundamental principles like conservation of momentum and energy.
This enables advancements in fields such as automotive safety, astrophysics, and material science. Insights from collision studies are crucial for designing safer vehicles and understanding cosmic events like planetary formation.
Provide a real-life application of studying collisions.
Designing of airbags in vehicles, which help minimize impact forces and reduce injuries during accidents.
Airbags absorb energy and increase the collision time, thereby reducing the force experienced by passengers. They work by extending the time of collision, lowering the force experienced by passengers according to F= Δp/Δt.
Define:
Elastic collision
Collision in which both momentum and kinetic energy are conserved.
Elastic collisions typically occur in systems where no energy is lost to deformation, heat, or sound.
Fill in the blank:
In an elastic collision, the objects _______ off each other after impact, maintaining their individual kinetic energies.
bounce
In contrast to inelastic collisions, the objects do not stick together in elastic collisions.
What are the equations related to elastic collisions?
Momentum conservation
- m1v1+m2m2=m1v’1+m2v’2
Kinetic energy conservation
- (1/2)m1v1²+(1/2)m2v2²=(1/2)m1v’1²+(1/2)m2v’2²
m1, m2 are the masses of the objects
v1, v2 are the initial velocities
v1’, v2’ are the final velocities after the collision
Fill in the blanks:
In an elastic collision, both ______ and ______ energy are conserved.
momentum; mechanical
Elastic collisions typically occur in idealized scenarios, where no energy is lost to heat, sound, or deformation.
Give one real-world example of an elastic collision.
Billiard balls colliding on a pool table.
The balls rebound with minimal loss of kinetic energy, approximating an elastic collision.
Define:
Inelastic collision
A type of collision where momentum is conserved, but kinetic energy is not.
Some energy is transformed into heat, sound, or deformation, leading to a loss of mechanical energy from the system. Examples include car crashes or objects that deform during the impact.
What happens in a perfectly inelastic collision?
The colliding objects stick together after the collision, moving as one combined object.
This results in the maximum loss of kinetic energy while conserving momentum.
What is the inelastic collision formula?
m1v1 + m2v2= (m1 + m2)vf
Where m1 and m2 are the masses of the two objects, v1and v2 are their initial velocities, and vf is the final velocity of the combined mass after the collision.
Explain the difference between elastic and inelastic collisions.
- In elastic collisions, both momentum and mechanical energy are conserved.
- In inelastic collisions, momentum is conserved, but mechanical energy is not.
Elastic collisions are idealized, typically involving objects like billiard balls.
What is meant by momentum conservation in the context of collisions?
Total momentum of a system remains constant before and after a collision, provided no external forces act on it.
This principle is used in analyzing both elastic and inelastic collisions.
What does mechanical energy conservation refer to during a collision?
The idea that the total mechanical energy (kinetic + potential) of a system remains constant during an elastic collision.
In inelastic collisions, mechanical energy is not conserved due to energy loss in forms like heat.
Explain why momentum is conserved in both elastic and inelastic collisions.
Because there is no net external force acting on the system.
This principle is a direct result of Newton’s Third Law of Motion.
List two factors that could cause momentum not to be conserved in a real-world collision.
- External forces, such as friction.
- Energy lost to sound, heat, or deformation.
These factors are often present in non-ideal conditions.
True or false:
In inelastic collisions, mechanical energy is conserved.
False
In inelastic collisions, mechanical energy is not conserved, although momentum is. Some energy is transformed into other forms, such as heat or sound, during inelastic collisions.
Explain why energy is lost in an inelastic collision.
Some of the mechanical energy is transformed into heat, sound, or deformation of the objects involved.
This is why the kinetic energy after an inelastic collision is less than before the collision.
Why is energy conserved in elastic collisions?
Kinetic energy and momentum are preserved because no energy is lost as heat or deformation.
Elastic collisions are idealized; real-world collisions often lose energy.
Fill in the blank:
In elastic collisions, the total ______ energy before and after the collision is the same.
mechanical
The mechanical energy remains unchanged only if the collision is perfectly elastic.
Define:
One-dimensional collision
Occurs along a straight line, where the objects collide and move in the same line.
Momentum is conserved in one dimension, but the analysis is simpler than in two dimensions.
What is the main challenge in analyzing two-dimensional collisions compared to one-dimensional collisions?
Momentum conservation must be applied separately to both the x and y directions, making the analysis more complex.
Additionally, the final velocities of the objects need to be resolved into components.
A hockey puck strikes another puck at an angle. What principles determine the final velocities?
Conservation of momentum in both x and y directions.
Elastic or inelastic properties also affect the final outcome.
Two cars collide at an intersection, one moving north and the other east. Explain how their post-collision velocities are determined.
By resolving their momenta into perpendicular components and conserving total momentum.
This is a two-dimensional inelastic collision problem.
What example illustrates the loss of mechanical energy due to friction in the context of collisions?
When a car skids to a stop after a collision, mechanical energy is lost as heat and sound due to friction between the tires and the road.
Friction converts kinetic energy into non-mechanical forms, reducing the total mechanical energy of the system.
What is the effect of collision time on the force experienced by an object?
Shorter collision times result in higher forces experienced by the object.
This is explained by the impulse-momentum theorem: Ft = Δp.
How does the center of mass behave during a collision?
It continues to move with the same velocity before and after the collision, provided no external forces act on the system.
The center of mass behaves as though all mass is concentrated at a single point, moving in a straight line.
What is the difference between a collision and an explosion in terms of momentum?
- In a collision, momentum is redistributed between objects.
- In an explosion, momentum is distributed outward as fragments move in different directions.
The total momentum of the system is conserved in both cases. Explosions often involve stored energy release, causing the fragments to separate.
In which type of problems do we use the equation for the conservation of momentum?
Ones that involve collisions or explosions, where no external forces act on the system.
It helps to calculate velocities before and after the collision. Momentum is conserved in both elastic and inelastic collisions, as well as in explosions.
In which type of problems do we use the equation for the conservation of kinetic energy?
In problems involving elastic collisions, where no energy is lost to deformation, heat, or sound.
It allows us to determine the velocities of objects after the collision. In inelastic collisions, kinetic energy is not conserved, so this equation is not applicable.
When are the conservation of momentum and conservation of kinetic energy equations used when studying collisions?
Both equations are used in problems involving elastic collisions, where both momentum and kinetic energy are conserved.
The conservation of momentum is used to relate the velocities of the objects before and after the collision, while the conservation of kinetic energy helps to ensure no energy is lost during the process.
