[SOLVED] SPH4U – Physics for University Test 6 – Unit 5 Matlab

SPH4U – Physics for University

Test 6 – Unit 5

Modern Physics

Multiple Choice – ***Circle one choice for each question.***

1.  (10 points) [K, T]

(a)  Which of the following is NOT a feature of an inertial frame of reference?

A.  Force

B.  Energy

C.  Psuedo-force

D.  Time

(b)  If you observe a light beam moving in the same direction whilst travelling half the speed of light, at what velocity would you register the beam of light?

A.  3 × 108 m/s    B.  1.5 × 108 m/s C.  4.5 × 108 m/s D.  0m/s

(c)  The idea of simultaneityin relativity states that

A.  Time travels linearly and all events occur in order.

B.  The time/order in which events happen can be different depending on the frame of reference.

C.  The distance traveled by light affects the time in which it takes for events to occur.

D.  Time and space occur simultaneously regardless of the frame of reference.

(d)  Relativistic effects are accounted for in measurements of time, space and momentum by using

A.  The speed of light.  B.  The Lorentz factor. C.  Planck’s constant. D.  The mass-energy equivalency.

(e)  The mass of an atom is less than the sum of it’s parts – this is a conversion of mass into .

A.  light.

B.  nothing.

C.  spin.

D.  binding energy.

(f)  Mass-energy equivalence is best represented by which of the following equations?

A.  E = 2/1mv2

B.  P = mv

C. E = mc2

D. EU = 2/1k∆x2

(g)  Which of the following forces are responsible for holding atmoic nuclei together?

A.  Strong force

B.  Weak force

C.  Electromagnetic force

D.  Gravitational force

(h)  Light atomic nuclei are more likely to undergo under high temperatures and pressure.

A.  nuclear fission B.  nuclear decay

C.  nuclear radiation D.  nuclear fusion

(i) is the only form of radiation in which an anti-neutrino (ν-) is formed.

A.  Alpha (α) decay

B.  Gamma (γ) decay

C.  Electron capture

D.  Beta (β) minus decay

(j)  Radioactive isotope decay/time is measured in which unit?

A.  Seconds (s)

B.  Half lives (t)

C.  Becquerel (bq)

D.  Joules (J)

Short Answers – ***Give complete answers, SHOW ALL OF YOUR WORK, don’t forget to use GRASP – Given, Required, Analysis, Solve, Paraphrase.***

2.  (10 points) [C, A] A UFO travels passed the Earth at a speed of 0.88C with respect to the Earth.

(a)  Calculate how fast the spaceship is going in m/s (2 pts)

(b)  An event observed on the surface of the Earth from the spaceship takes 72hours.  Calculate how long the same event takes on Earth. (4 pts)

(c)  The discrepancy in time taken is due to a phenomenon known as time dilation?  In the space given below, explain how time dilation occurs at speeds of light. You may also draw a diagram to help in your explanation. (4 pts)

3.  (10 points) [A, T] An indestructible cord of rope is measured to have a length of 6.45m at rest.

(a)  ) The rope is placed on a machine that starts to oscillate the rope at 2.3 × 108 m/s. Calculate the new length of the rope due to length contraction. (3 pts)

(b)  Calculate the Lorentz factor of the rope under length contraction. (2 pts)

(c)  Using your understanding of the v  =  d/t formula,justify the existence of length contraction under time dilation. (5 pts)

4.  (15 points) [K, C] In the early 1900’s, a Physicist named Albert Einstein came up with two theories that would change the way we understood the universe.

(a)  The theory of general relativity states that there is equivalence in both inertial and non-inertial frames (the law of equivalence). Using Einsteins example of the space elevator, show that gravitational mass and inertial mass are equal. (5 pts)

(b)  With the theory of general relativity, we understand there is a relationship between space, time, and gravity. Explain the following relationships:

i) What is the relationship between space and time? (3 pts)

ii) What is the relationship between gravity and space-time? (3 pts)

(c)  We can often see the force of gravity at work through the attraction between masses, but relativity helped explained the cause of gravity was.  In the space below, explain how gravitational force is formed in the context of special and general relativity. (4 pts)

5.  (12 points) [K, C] The speed of light in a vacuum is known as the speed limit of the universe, this is because no object with mass can reach this velocity, and no objects with 0 mass can surpass it.

(a)  By using the idea of momentum, we can see how an object with mass can’t surpass the speed of light. Define momentum in the space given below. (2 pts)

(b)  Momentum at relativistic speeds can be expressed using the following equation:

ρ = mv

√1 –

i) Using the expression above, explain what happens as we approach the speed of light. (3 pts)

ii) Using the expression above, show how an object with mass can’t exceed the speed of light. (3 pts)

(c)  The time dilation formula is also another way of proving that c is the upper limit of the universe.

Use the formula above to show what happens when we are travelling at the speed of light and beyond. (Hint: Write in context of the law of causality). (4 pts)

6.  (10 points) [C, A] One of the most famous equations in all of Physics (and possibly science) is Einsteins’ mass- energy equivalence equation E = mc2 .

(a)  The mass-energy equivalence formula states that the two quantities are inter-changeable. In the space below, outline an appropriate law of conservation that includes both energy and mass. (2 pts)

(b)  The atomic mass of a carbon-12 atom is  12 atomic units (au), however when we sum the mass of each individual particle, (6 protons, neutrons and electrons), we get a mass of 12.11 au. What is the cause of the discrepancy in mass? (3 pts)

(c)  Calculate the rest energy of a carbon-12 atom (mass = 1.998 × 10-26kg). Give your answer in electron volts (1eV = 1 × 10-19J) (2 pts)

(d)  The carbon-12 atom is then put into a particle accelerator and sped up to 75% the speed of light.  Calculate the energy of the carbon-12 atom (take relativistic effects into account) (3 pts)

7.  (13 points) [C, T] We can see the application of the mass-energy equivalence principle during nuclear reactions; more specifically we see that mass can be formed into energy.

(a)  Nuclear reactions can be categorised into two forms; nuclear fission, and nuclear fusion.  Fill in the blanks below with the most appropriate answers.

i) Nuclear is constructive in nature, and occurs at high and . It is mostly seen in nuclei that are than iron-56. (2 pts)

ii) Nuclear is destructive in nature, and occurs when there is an imbalance in the electro- static and force in the nucleus.  It is mostly seen in nuclei that are than iron-56. (2 pts)

(b)  There are 5 forms of radioactive decay that can occur as a result of nuclear reactions. In the problem below, match the type of decay to its’ description. (5 pts).

(c)  An atom of uranium-235 undergoes radioactive decay and releases 3.2 × 10-11J of energy.  Calculate the change in mass due to mass-energy equivalence. (4 pts)

8.  (10 points) [A, T] Nuclear decay is measured in terms of it’s progression towards stability.

(a)  A sample of sodium-22 has a half life of 2.6 years. The samples sees a reduction inactivity from 400kbq to 80kbq. Calculate the amount of time taken for this reduction inactivity. (4 pts)

(b)  Radioactive materials like sodium-22 will generally undergo exponential decay (as see in the graph below).

Explain why the activity of a sample is always exponential in terms of the rate of decay.(3 pts)

(c)  When weighed, the initial sample of sodium-22 had a mass of 0.0380kg.  Calculate the mass of the sample after 10 years. (3 pts)

9.  (10 points) [K,  T] Energy to mass conversion can be  seen as a phenomena during high energy collisions of particles – this is being studied at the Large Hadron Collider in Switzerland.

(a)  At high energy collisions, we see the formation of matter/anti-matter pairs. In the space below, describe the difference between matter and anti-matter. (3 pts)

(b)  Matter and anti-matter pairs are formed in equal amounts, but will not last very long – explain why this may be the case. (3 pts)

(c)  In the spaces given, fill in the blanks with the appropriate information about matter/anti-matter pairs. (4 pts)

matter: Proton (1+) antimatter: (     )

matter: (    ) antimatter: Positron (+1)

matter: Neutrino (    ) antimatter: Anti-neutrino (     )