SPH4U Physics
Independent Study
Special Relativity
Due Date:
Thursday June 1 2023
Evaluation:
a) Assignment 25 marks b) Quiz 15 marks . . . Total 40 marks
To be included as part of the Culminating Activities mark
Any notes you take, and your assignment, can be used during the quiz!!
References:
Physics 12 – Chapter 11:Relativity
Independent Research
Objectives:
Students are expected to be able to . . .
1. Summarize the key features of the Michelson-Morley experiment and relate the
experimental results to Einstein’s two postulates.
2. Discuss the reasons for the hypothesis of an ether in the 19th century and indicate how
this concept was affected by the Michelson-Morley experiment.
3. State Einstein’s two postulates and discuss how these affect the concept of an absolute
frame of reference as used by Newton.
4. Define simultaneity and show how the two postulates eliminate any absolute concept of
simultaneity for all observers.
5. Explain time dilation and define and use the symbols t and to in the formula
𝑡𝑜
𝑡=
𝑣2
√(1 − 2 )
𝑐
6. Explain length contraction and define and use the symbols L and Lo in the formula
𝐿 = 𝐿𝑜 √(1 −
𝑣2
)
𝑐2
7. Explain mass increase and define and use the symbols m and mo in the formula
𝑚𝑜
𝑚=
𝑣2
√(1 − 2 )
𝑐
2
8. Explain the significance of Einstein’s formula E = mc for energy transformations.
9. Solve problems using all four equations.
Expectations:
Answers to the following questions are to be completed and submitted via
the appropriate Google Classroom drop box.
1. Briefly discuss the reasons for the hypothesis of an ether in the 19th century.
(3 marks)
2. If you were on a spaceship travelling at 0.50 c away from a star, at what speed would the
starlight pass you?
(1 mark)
3. Explain why the apparent failure of the Michelson-Morley experiment was actually a
success.
(2 marks)
4. Is there a situation where two events, which are simultaneous for one observer, can be
simultaneous for a second observer who is moving relative to the first? Explain.
(3 marks)
5. What happens to the mass of an electron as it is accelerated close the speed of light?
Could the electron ever be made to travel at the speed of light? Explain why it can or
cannot travel at 1.0 c.
(3 marks)
6. A friend borrows your red “Ferrari Spaceship Model X-19” capable of travelling at 0.85c.
The Ferrari is measured to be 5.6 m high and 18 m long in a stationary reference frame.
a) How long would you say the Ferrari is as it sped by you at maximum speed?
(1 mark)
b) Your friend has been gone for 2.0 h your time. How much time does he believe
has elapsed?
(1 mark)
7. Is there a change in mass, time, or length at a normal speed of 100 km/h? Use the Lorentz
equations to support your explanation.
(2 marks)
8. Explain how the equation 𝐸 = 𝑚𝑐 2 is consistent with Law of Conservation of Energy.
(2 marks)
9. A 520 m long (measured when the spaceship is stationary) spaceship passes by the Earth.
What length would the people on Earth say the spaceship was as it passed the Earth at
0.87c?
(1 mark)
10. What speed would an object have to travel to increase its mass by 50%?
(2 marks)
11. It takes 2.3 × 1010 𝐽 of energy to operate a long train for 1.0 h. For how long could you
operate this train if 45 kg of matter could be converted into pure energy?
(2 marks)
12. A spaceship has been gone from the Earth for a total time of 5 years ship time. The
people on the Earth have measured the time for the ship to be away to be 25 years. How
fast was the ship travelling?
(2 marks)