Question

a) How fast must a meter stick be moving if its length is observed to shrink to 0.6 m? b) With what speed will a clock have to be moving in order to run at a rate that is one-half the rate of a clock at rest?

Answer 1

A)

0.8 c

B)

0.87 c

Step-by-step explanation:

A)

L₀ = Original length of the meter stick = 1 m

L = Length observed = 0.6 m

`v` = speed of the meter stick

Using the equation

`L = L_(o) \sqrt{1 - \left ( (v)/(c) \right )^(2)}`

`0.6 = 1 \sqrt{1 - \left ( (v)/(c) \right )^(2)}`

`0.36 = 1 - \left ( (v)/(c) \right )^(2)`

`v` = 0.8 c

B)

T₀ = Time of the clock at rest = t

T = Time of the clock at motion = (0.5) t

`v` = speed of the clock

Using the equation

`T = T_(o) \sqrt{1 - \left ( (v)/(c) \right )^(2)}`

`0.5 t = t \sqrt{1 - \left ( (v)/(c) \right )^(2)}`

`0.5  =  \sqrt{1 - \left ( (v)/(c) \right )^(2)}`

v = 0.87 c