Exploring Collisions
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Questions and Answers

What is the equation for conservation of kinetic energy in an elastic collision?

$K_i = K_f + \ rac{1},{2}m_1v_{1i}^2 + \ rac{1},{2}m_2v_{2i}^2$

How many unknown quantities can be solved if no more than two of the seven quantities in Equations 9.25 and 9.26 are unknown?

Four

If the collision is inelastic, is kinetic energy conserved?

No

What is the equation for momentum conservation in the x direction?

<p>$p_{ix} = p_{fx}$</p> Signup and view all the answers

What is the equation for momentum conservation in the y direction?

<p>$p_{iy} = p_{fy}$</p> Signup and view all the answers

In an elastic collision, what is the relationship between the total kinetic energy before and after the collision?

<p>They are equal</p> Signup and view all the answers

What does Equation 9.27 represent?

<p>Conservation of kinetic energy in an elastic collision</p> Signup and view all the answers

What is the equation for the x component of momentum?

<p>$p_x = mv_x$</p> Signup and view all the answers

What is the equation for the y component of momentum?

<p>$p_y = mv_y$</p> Signup and view all the answers

What should you do once you have determined your result?

<p>Check if the answers are consistent with the mental and pictorial representations and if they are realistic</p> Signup and view all the answers

What is conserved in a collision of two particles?

<p>momentum</p> Signup and view all the answers

In what directions is momentum conserved in a collision of two particles?

<p>x, y, and z</p> Signup and view all the answers

What are the component equations for conservation of momentum in a two-dimensional collision?

<p>$m_1v_{1ix} + m_2v_{2ix} = m_1v_{1fx} + m_2v_{2fx}$ and $m_1v_{1iy} + m_2v_{2iy} = m_1v_{1fy} + m_2v_{2fy}$</p> Signup and view all the answers

What is a glancing collision?

<p>An event where particle 1 and particle 2 collide and move at angles with respect to the horizontal</p> Signup and view all the answers

What is the equation for conservation of momentum in the x direction in a glancing collision?

<p>$\Delta p_x = 0 \implies p_{ix} = p_{fx} \implies m_1v_{1i} = m_1v_{1f}\cos(u) + m_2v_{2f}\cos(f)$</p> Signup and view all the answers

What is the equation for conservation of momentum in the y direction in a glancing collision?

<p>$\Delta p_y = 0 \implies p_{iy} = p_{fy} \implies 0 = m_1v_{1f}\sin(u) - m_2v_{2f}\sin(f)$</p> Signup and view all the answers

Why does the equation for conservation of momentum in the y direction have a minus sign?

<p>After the collision, particle 2 has a downward y component of velocity</p> Signup and view all the answers

What are the symbols v in the equations for conservation of momentum?

<p>Speeds, not velocity components</p> Signup and view all the answers

True or false: The direction of the component vector is indicated explicitly with plus or minus signs.

<p>True</p> Signup and view all the answers

True or false: If the collision is elastic, we can use Equation 9.17 (conservation of kinetic energy) with $v_{2i}=0$.

<p>True</p> Signup and view all the answers

True or false: In an elastic collision, kinetic energy is conserved.

<p>True</p> Signup and view all the answers

True or false: In an inelastic collision, kinetic energy is conserved.

<p>False</p> Signup and view all the answers

True or false: If the collision is perfectly inelastic, the final velocities of the two objects are equal.

<p>True</p> Signup and view all the answers

True or false: In a glancing collision, momentum is conserved in the x direction.

<p>False</p> Signup and view all the answers

True or false: In a glancing collision, momentum is conserved in the y direction.

<p>True</p> Signup and view all the answers

True or false: If the collision is inelastic, additional information is probably required.

<p>True</p> Signup and view all the answers

True or false: The equation for conservation of momentum in the x direction in a glancing collision is $p_{ix} = p_{fx}$.

<p>False</p> Signup and view all the answers

True or false: The equation for conservation of momentum in the y direction in a glancing collision is $p_{iy} = p_{fy}$.

<p>True</p> Signup and view all the answers

True or false: Momentum is conserved in each of the x, y, and z directions in a collision of two particles.

<p>True</p> Signup and view all the answers

True or false: The game of billiards involves multiple collisions of objects moving on a two-dimensional surface.

<p>True</p> Signup and view all the answers

True or false: In a two-dimensional collision, there are two component equations for conservation of momentum.

<p>True</p> Signup and view all the answers

True or false: In a glancing collision, particle 1 moves at an angle u with respect to the horizontal and particle 2 moves at an angle f with respect to the horizontal.

<p>True</p> Signup and view all the answers

True or false: The law of conservation of momentum can be applied in component form for a glancing collision.

<p>True</p> Signup and view all the answers

True or false: The initial y component of momentum of a two-particle system is always zero in a glancing collision.

<p>True</p> Signup and view all the answers

True or false: The equation Dp x = 0 represents the conservation of momentum in the x direction for a glancing collision.

<p>True</p> Signup and view all the answers

True or false: The equation Dp y = 0 represents the conservation of momentum in the y direction for a glancing collision.

<p>True</p> Signup and view all the answers

True or false: The equation Dp y = 0 includes a minus sign because after the collision, particle 2 has a downward y component of velocity.

<p>True</p> Signup and view all the answers

True or false: In a glancing collision, the total kinetic energy before and after the collision is conserved.

<p>False</p> Signup and view all the answers

Which equation can be used to determine the motion after an elastic collision?

<p>Equation 9.27</p> Signup and view all the answers

Which of the following is true about solving a problem involving collisions between two particles in two dimensions?

<p>The system of particles must be isolated</p> Signup and view all the answers

What is the equation for conservation of momentum in the x direction in a glancing collision?

<p>$p_{ix} = p_{fx}$</p> Signup and view all the answers

How many unknown quantities can be solved if no more than two of the seven quantities in Equations 9.25 and 9.26 are unknown?

<p>Three</p> Signup and view all the answers

What is the equation for conservation of kinetic energy in an elastic collision?

<p>$K_i = K_f$</p> Signup and view all the answers

True or false: If the collision is inelastic, kinetic energy is conserved.

<p>False</p> Signup and view all the answers

What are the component equations for conservation of momentum in a two-dimensional collision?

<p>$p_{ix} = p_{fx}$ and $p_{iy} = p_{fy}$</p> Signup and view all the answers

True or false: The equation $Dp_y = 0$ includes a minus sign because after the collision, particle 2 has a downward y component of velocity.

<p>True</p> Signup and view all the answers

True or false: In a glancing collision, momentum is conserved in the x direction.

<p>True</p> Signup and view all the answers

What should you do once you have determined your result?

<p>Check to see if your answers are consistent with the mental and pictorial representations</p> Signup and view all the answers

Which equations represent the conservation of momentum in the x and y directions for a two-dimensional collision?

<p>$m_1v_{1ix} + m_2v_{2ix} = m_1v_{1fx} + m_2v_{2fx}$ and $m_1v_{1iy} + m_2v_{2iy} = m_1v_{1fy} + m_2v_{2fy}$</p> Signup and view all the answers

What is the equation for the x component of momentum in a glancing collision?

<p>$m_1v_{1ix} + m_2v_{2ix} = m_1v_{1fx} + m_2v_{2fx}$</p> Signup and view all the answers

What is the equation for the y component of momentum in a glancing collision?

<p>$m_1v_{1iy} + m_2v_{2iy} = m_1v_{1fy} + m_2v_{2fy}$</p> Signup and view all the answers

What is the equation for conservation of kinetic energy in an elastic collision?

<p>$m_1v_{1i}^2 + m_2v_{2i}^2 = m_1v_{1f}^2 + m_2v_{2f}^2$</p> Signup and view all the answers

What is a glancing collision?

<p>A collision in which the objects move at an angle with respect to the horizontal after the collision.</p> Signup and view all the answers

What is conserved in a collision of two particles?

<p>Momentum</p> Signup and view all the answers

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