In inelastic collisions, ________ is not conserved.
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net external
However, momentum is conserved even when forces act at a distance as long as there are no ________ forces.
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elastic collision
In a(n) ________, kinetic energy is conserved.
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○ Common Error
________: The initial kinetic energy of the bullet can not be equated to the final energy stored in the spring because mechanical energy is not conserved during the collision; mechanical energy is conserved after the bullet lodges in the block.
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uniform mass density
The object has ________ and a radius of r. Solution ● Symmetry about the y- axis dictates that the x- coordinate of the center of mass must be zero.
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conservation of momentum
● Always use ________ when solving a collision problem and conservation of energy if the collision is elastic.
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elastic collision
The angle between the paths of two balls of equal mass after a(n) ________ where one ball was initially at rest will always be 90°.
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● Relationship between impulse and force
the impulse-momentum theorem
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Example 6.1.1 Problem
During a collision with a wall lasting from t = 0 to t = 2 s, the force acting on a 2 kg object is given by the equation
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Example 6.1.2 Problem
Compare a person falling on a bare gym floor with a person falling on a mat
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Example 6.1.3 Problem
A bullet of mass 0.005 kg moving at a speed of 100 m/s lodges within a 1 kg block of wood resting on a frictionless surface and attached to a horizontal spring of k = 50 N/m
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b) At this point, we have a standard mass and spring problem
○ A mass of 1.005 kg moves with an initial velocity of 0.5 m/s when the spring of k = 50 N/m is at its equilibrium position
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○ Common Error
The initial kinetic energy of the bullet cannot be equated to the final energy stored in the spring because mechanical energy is not conserved during the collision; mechanical energy is conserved after the bullet lodges in the block
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Example 6.1.4 Problem
A variable force F(t) acts on an object of mass m that is initially at rest for a time interval t. a) Find an expression for the final velocity by calculating the impulse and relating it to the momentum
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Example 6.1.5 Problem
Particle C collides and sticks to particle S. If the particles have masses mC and mS and
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● Inserting this into the second equation and solving via the quadratic equation yields two answers
v2 = −1 m/s and v2 = 1.769 m/s
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This certainly makes sense
Everything is conserved between the initial situation and itself
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● Thus, the second solution is the one we are interested in
The 10 kg mass has a final velocity of 1.769 m/s to the right
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● Tip
Momentum is a vector
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6.2
Center of Mass ● The center of mass is defined to be the weighted average of the location of mass in a system
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Solution ● Computing the center of mass of a group of point masses is straightforward
simply plug into the above formulas
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● Answer check
We note that each of these coordinates lies somewhere between the corresponding coordinates of the masses
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○ This involves a common theme in Physics C
moving to a differential level
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● Symmetry shortcut
Any plane of symmetry, mirror line, axis of rotation, or point of inversion must contain the center of mass
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○ If you think of the center of mass as a weighted average, it makes sense
If there are identical mass distributions on either side of a plane, axis, or point, the weighted average must lie on that plane, axis, or point
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Example 6.2.3 Problem
Calculate the center of mass of this object, with the center of the larger circle as the origin of your coordinate system
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● This is an alternative derivation of the conservation of momentum for a system of particles
If the net force on a system of particles is zero, the total momentum of the system remains constant
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\
Momentum
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Momentum
It obeys superposition such that the net momentum of a collection of objects is the vector sum of the momentum of each object
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**Linear momentum**
A vector parallel to velocity
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Relationship Between Force and Momentum
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Definition of Impulse
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**elastic collision**
In this collision, kinetic energy is conserved.
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**inelastic collision**
In **this collision**, kinetic energy is not conserved.
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**totally inelastic collision**
In this collision, kinetic energy is also not conserved, and the two objects remain stuck together after the collision.
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center of mass
defined to be the weighted average of the location of mass in a system.
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