The approach to two-dimensional collisions is to choose a convenient coordinate system and break the motion into components along perpendicular axes. Choose a coordinate system with the
-axis parallel to the velocity of the incoming particle.
Two-dimensional collisions of point masses where mass 2 is initially at rest conserve momentum along the initial direction of mass 1 (the
-axis), stated by
and along the direction perpendicular to the initial direction (the
-axis) stated by
.
The internal kinetic before and after the collision of two objects that have equal masses is
Point masses are structureless particles that cannot spin.
Conceptual questions
[link] shows a cube at rest and a small object heading toward it. (a) Describe the directions (angle
) at which the small object can emerge after colliding elastically with the cube. How does
depend on
, the so-called impact parameter? Ignore any effects that might be due to rotation after the collision, and assume that the cube is much more massive than the small object. (b) Answer the same questions if the small object instead collides with a massive sphere.
Problems&Exercises
Two identical pucks collide on an air hockey table. One puck was originally at rest. (a) If the incoming puck has a speed of 6.00 m/s and scatters to an angle of
,what is the velocity (magnitude and direction) of the second puck? (You may use the result that
for elastic collisions of objects that have identical masses.) (b) Confirm that the collision is elastic.
(a) 3.00 m/s,
below
-axis
(b) Find speed of first puck after collision:
Verify that ratio of initial to final KE equals one:
Confirm that the results of the example
[link] do conserve momentum in both the
- and
-directions.
A 3000-kg cannon is mounted so that it can recoil only in the horizontal direction. (a) Calculate its recoil velocity when it fires a 15.0-kg shell at 480 m/s at an angle of
above the horizontal. (b) What is the kinetic energy of the cannon? This energy is dissipated as heat transfer in shock absorbers that stop its recoil. (c) What happens to the vertical component of momentum that is imparted to the cannon when it is fired?
(a)
(b)
(c) The ground will exert a normal force to oppose recoil of the cannon in the vertical direction. The momentum in the vertical direction is transferred to the earth. The energy is transferred into the ground, making a dent where the cannon is. After long barrages, cannon have erratic aim because the ground is full of divots.
Professional Application
A 5.50-kg bowling ball moving at 9.00 m/s collides with a 0.850-kg bowling pin, which is scattered at an angle of
to the initial direction of the bowling ball and with a speed of 15.0 m/s. (a) Calculate the final velocity (magnitude and direction) of the bowling ball. (b) Is the collision elastic? (c) Linear kinetic energy is greater after the collision. Discuss how spin on the ball might be converted to linear kinetic energy in the collision.
Professional Application
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei
from gold-197 nuclei
. The energy of the incoming helium nucleus was
, and the masses of the helium and gold nuclei were
and
, respectively (note that their mass ratio is 4 to 197). (a) If a helium nucleus scatters to an angle of
during an elastic collision with a gold nucleus, calculate the helium nucleus’s final speed and the final velocity (magnitude and direction) of the gold nucleus. (b) What is the final kinetic energy of the helium nucleus?
(a)
at
(b)
Professional Application
Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and is approaching at
due south. The second car has a mass of 850 kg and is approaching at
due west. (a) Calculate the final velocity (magnitude and direction) of the cars. (b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.) Note that because both cars have an initial velocity, you cannot use the equations for conservation of momentum along the
-axis and
-axis; instead, you must look for other simplifying aspects.
Starting with equations
and
for conservation of momentum in the
- and
-directions and assuming that one object is originally stationary, prove that for an elastic collision of two objects of equal masses,
as discussed in the text.
We are given that
. The given equations then become:
and
Square each equation to get
Add these two equations and simplify:
Multiply the entire equation by
to recover the kinetic energy:
Integrated Concepts
A 90.0-kg ice hockey player hits a 0.150-kg puck, giving the puck a velocity of 45.0 m/s. If both are initially at rest and if the ice is frictionless, how far does the player recoil in the time it takes the puck to reach the goal 15.0 m away?
Questions & Answers
I'm interested in biological psychology and cognitive psychology
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills