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S4.6 Collisions

[A] Context

ATwo Ball Collisions

Examples

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Examples

Collisions range widely in scale, from the impact of comets on planets, through the contact of a tennis ball with a racquet, to the collision of photons with our eyes.
 

Commentary

Commentary

Note that a collision does not require a “crash” or physical contact. Eg. When a spacecraft swings round a planet to pickup speed, this can also be regarded as a collision.

Much of modern experimental particle and condensed matter physics relies on collisions or ‘scattering’ between a beam of particles and the physical system of interest. In fact most of our knowledge of the sub-molecular world comes from such experiments. Conservation of linear momentum and energy are key factors in interpreting the results.

 

[B] Impulse

For a 1D collision, the impulse is the area under the F(t) curve describing the collision
Graphic - No title - avforce

Demo

Demo

Demonstration : Raw eggs and impulse (!)
 

[C] Inelastic collisions

[D] Elastic collisions

Demo

Demo

Demonstrations of various elastic and inelastic collisions using air track / air table
 
AThe Virtual Air Track

[E] Problem solving tactics for collisions

Worked example

Worked example

Two blocks of mass 300 g and 200 g are moving towards one another along a horizontal frictionless surface with velocities of 50 cm s-1 and 100 cm s-1 respectively.

  • [(a)] If the blocks collide and stick together, find their final velocity.
  • [(b)] Find the loss of kinetic energy during the collision.
  • [(c)] Find the final velocity of each block if the collision is completely elastic.

Solution

(a) Since the surface is frictionless, it is isolated in the direction of motion and so momentum is conserved:

\[ \vec{p}_{1i}+\vec{p}_{2i}=\vec{p}_{1f}+\vec{p}_{2f} \]
Hence

\begin{eqnarray*} %%%Was makeeqnarraystar; label was blocks1 {\xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{(0.3 \times 0.5) - (0.2 \times 1.0)}} & = & {\xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{(0.3+0.2) \times v_f}} \end{eqnarray*}

So vf=-0.1ms-1

(b)  

\begin{eqnarray*} %%%Was makeeqnarraystar; label was blocks2 K_i &=& {\xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{0.5\left[0.3\times (0.5)^2 + 0.2\times (1.0)^2\right]}} \\ &=& 0.1375 J \\ K_f &=& {\xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{0.5\times (0.3+0.2) \times (-0.1)^2}} \\ &=& 0.0025 J \end{eqnarray*}

Hence the loss in kinetic energy is 0.135J.

(c) For an elastic collision, both momentum and kinetic energy are conserved.

\begin{eqnarray*} %%%Was makeeqnarraystar; label was blocks3 m_1v_{1i}+m_2v_{2i} &=& m_1v_{1f}+m_2v_{2f}\\ 0.5(m_1v_{1i}^2+m_2v_{2i}^2) &=& 0.5( m_1v_{1f}^2+\times m_2v_{2f}^2)\\ \end{eqnarray*}

Given m1,m2,v1i,v2i, can solve to find v1f=-0.7ms-1, v2f=0.8ms-1.

 
TThrowing Balls in Carts

Learning Resources

Textbook: HRW 9.6 and 9.8-9.11
Course Questions:
Self-Test Questions: