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Unformatted text preview: The Relativity of Time
*Relative motion change change the rate at which time passes. *The amount by which a measured time interval is greater than Δto, the proper time, is called time dilation. Example
Your starship passes Earth with a relative speed of 0.9990c. After traveling 10.0 y (your time), you stop, turn, and travel back to Earth with the same relative speed. The trip takes another 10.0 y (your time). How long does the round trip take according t o measurements made on Earth? (Neglect effects of accelerations involved in turning, stopping and getting back up to speed) Key Ideas: Δt = Δt o ⎛ v⎞ 1− ⎜ ⎟ ⎝ c⎠ and
2 β= v c γ= 1 1− β2 Δt = γΔt o 11/14/10 1 11/14/10 2 Twin Paradox The Relativity of Velocity Classical vOA = vOT + vTA
8.6 light-years Relativistic
Alice calculates: Ted calculates: vOA = vOT + vTA vv 1 + OT 2 TA c 11/14/10 3 11/14/10 4 1 The Relativity of Velocity Momentum
Classical If the car goes at 0.6c and the driver throws the rock with a speed of 0.8c, what is the velocity of the rock as observed by the girl? Relativistic vOA = vOT + vTA vv 1 + OT 2 TA c
5 11/14/10 6 11/14/10 Example What is mass?
Classical: Relativistic: ∑F a=
A satellite, initially at rest in deep space, explodes into two pieces. One piece has a mass of 150 kg and moves away from the explosion with speed 0.76c. The other piece moves away from the explosion in the opposite direction with a speed of 0.88c. Find the mass of the second piece of the satellite.
11/14/10 7 11/14/10 a= ∑F (1 − β ) mo 2 3/ 2 8 2 Kinetic Energy
Classical: Rest Energy
KE = mo c 2 1− β
2 KE = 1 mo v 2 2 − mo c 2 Relativistic: W = F Δx =
11/14/10 (1 − β ) mo a 2 3/ 2 Δx KE = mo c 2 1− β
2 − mo c 2
9 11/14/10 10 Example Energy is radiated by the Sun at the rate of 3.92 x1026 W. Find the corresponding decrease in the Sun’s mass for every second that it radiates. 11/14/10 11 3 ...
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