How Fast Must a Limo Travel Near Light Speed to Appear Shorter?

[jwoosley]

hey everyone I'm new here. you all seem great at physics and my teacher gave us these problems and i have no clue as to how to do them! please help me it is due tonight!

1.Natalie designs stretch limo that is 9 m long but appears to be only 5.000m long when driven at speeds near the speed of light. How fast must Natalie be going to make the limo appear this long to Morgan who is watching the new stretch limo?

2.The net result of a hydrogen fusion reaction is that four hydrogen atoms combine to form a helium atom. The mass lost when rest energy is converted into radiation energy in the reaction is 3.250x10-29 kg. How much radiation energy does this reaction produce?

 

[HallsofIvy]

1. If your physics teacher gave you this problem then he/she certainly expects you to know the "Lorentz contraction" formula. Try looking that up first in your text or notes. If you honestly can't find, get back to us.

2. Once again, this is just a matter of apply a (well known!) formula that connects energy and mass. Look for it in your book or notes and get back to us.

 

[jwoosley]

ok i found the formula: final length = original length * sq root (1- (v2/c2)), so i plugged this in, solved for velocity and got 290593262.9, and it wants the answer in the unit "c", is that correct then?

 

[jwoosley]

correction the answer is 249443825, so how do i put this in "c"? thanks!

 

[Artorius]

To place in terms of "c", divide your answer by the value for "c" itself, the speed of light, which is usually rounded to 300,000,000 m/s. The ratio is the fraction of the speed of light:

0.75c = three-quarters of the speed of light
0.5c = half of the speed of light
0.25c = quarter of the speed of light
.
.
etc.