1. Draw a Feynman diagram illustrating an electron scattering off a photon. Sol.

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Abigayle Thompson
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1 PHYSICS 3: Contemporary Physics I: HW Solution Key. Draw a Feynman diagram illustrating an electron scattering off a photon. e e e e There may be more than, but you need only draw.. P.6 A proton in an accelerator attains a speed of 0.88c. What is the momentum of the proton? First, let s compute the factor: v c So: p mv ( kg( m/s)(.) kg m/s 3. What is the factor of a particle moving at: (a) m/s Noting that this is 0.0c, and doing a little plug and chug: (0.0) but for future reference, there s a cool rule of thumb that you can use for small speeds: In this case, n /, and x v /c, so: lim ( + x 0 x)n + nx + v /c

2 (b) 0.5c This is not much less than the speed of light, so we need to use the full equation: v /c (c) 0.999c Ditto v /c For which of these can you assume non-relativistic physics? 4. Consider a kg block. What is the momentum if the speed is: (a) 0 m/s? This is non-relativistic, to. In this limit: p mv 0 kg m/s (b) m/s Because I care, you ll note that this is half the speed of light, and you already computed the gamma factor for this in the previous problem:.55. So: p mv ( kg)( m/s)(.55) kg m/s 5. A particle with a mass of 0 6 kg has a momentum of p kg m/s. How fast is it traveling? If you get an answer that s faster than the speed of light, you should at least consider the possibility that you ve made a mistake. We derived a nice inversion relation: First, note: p/m v + ( p mc ) p m 4 08 m/s

Note that this is not the speed. It s faster than light: so, plugging int: p mc.333 v 4 0 8 m/s + (.333) 6. P.4 a,d,f,g only.4 0 8 m/s 0.8c A 0.

3 Note that this is not the speed. It s faster than light: so, plugging int: p mc.333 v m/s + (.333) 6. P.4 a,d,f,g only m/s 0.8c A 0.7 kg block of ice is sliding by you on a very slippery floor at.5 m/s. As it goes by, you give it a kick perpendicular to its path. your foot is in contact with the ice block for.003 s. The block eventually slides at an angle of degrees from its original direction. The overhead view shown in Figure.54 is approximately to scale. The arrow represents the average force your toe applies briefly to the block of ice. a) Which of the possible paths shown in the diagram corresponds to the correct overhead view of the block s path? After you strike the block, it continues in a straight line, so B. d) What is the x component of the block s momentum after the kick? Same as original: p x.75 kg m/s f) Use your answers to the preceding questions to find the z component of the block s momentum after the kick (drawing a diagram is helpful). First, note that it initially has a momentum of: p i (0.7 kg)(.5 m/s)î.75 kg m/sî and afterwards, it s at a angle with the original. Thus: p y p x tan 0.404

4 so p y 0.404p x 0.7 kg m/s g) What was the magnitude of the average force you applied to the block? Since the y-component of momentum is: p y p y F t F p y t 0.7 kg m/s s 36.7 N 7. You are standing at the top of a 0m cliff (as shown), throwing stones over the edge. You throw a 0. kg stone at an angle of 30 degrees (π/6) above the horizontal with a speed of 0m/s. (a) Express the velocity of the stone in terms of individual x- and y- components in the instant after it leaves your hand. The individual components are: v x v 0 cos θ (0 m/s) cos(π/6) 8.66 m/s and so v y v 0 sin θ (0 m/s) sin(π/6) 5 m/s v , 5 m/s (b) How long after you throw it does it reach it s maximum height? The velocities are non-relativistic, so we have: At maximum height, v y 0. So: v y (t) v y,0 gt t max v y,0 g 5 m/s 0 m/s 0.5 s

5 (c) How long after you throw the stone does it take to hit the ground? y y 0 + v y,0 t gt This is a little tougher. We need to solve a quadratic equation for y 0. Quadratic formula time. If you have: at + bt + c 0 the solutions are: In our case: t b ± b 4ac a a g b v y,0 so: t c y 0 v y,0 ± vy 0 + gy 0 g 5 m/s ± 5 m /s + 00 m s 0 m/s 5 m/s ± 5 m/s 0 m/s s where I ve taken the solution. (d) How far from the edge of the cliff does the rock hit? The horizontal distance is: x v x,0 t 7.3 m

Planar Motion with Constant Acceleration

Planar Motion with Constant Acceleration 1. If the acceleration vector of an object is perpendicular to its velocity vector, which of the following must be true? (a) The speed is changing. (b) The direction