Question

Suppose the object moving is Dave, who hasamassofmo =66kgatrest. Whatis Daveâs mass at 90% of the speed of light? At 99% of the speed of light? At 99.9% of the speed of light? and How fast should Dave be moving to have a mass of 500 kg?

Answer 1

Step-by-step explanation:

Formula that relates the mass of an object at rest and its mass when it is moving at a speed v:

$m=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}$

Where :

m = mass of the oebjct in motion

$m_o$ = mass of the object when at rest

v = velocity of a moving object

c = speed of the light = $3\times 0^8 m/s$

We have :

1) Mass of the Dave = $m_o=66 kg$

Velocity of Dave ,v= 90% of speed of light = 0.90c

Mass of the Dave when moving at 90% of the speed of light:

$m=\frac{66 kg}{\sqrt{1-\frac{(0.90c)^2}{c^2}}}$

m = 151.41 kg

Mass of Dave when when moving at 90% of the speed of light is 151.41 kg.

2) Velocity of Dave ,v= 99% of speed of light = 0.99c

Mass of the Dave when moving at 99% of the speed of light:

$m=\frac{66 kg}{\sqrt{1-\frac{(0.99c)^2}{c^2}}}$

m = 467.86 kg

Mass of Dave when when moving at 99% of the speed of light is 467.86 kg.

3) Velocity of Dave ,v= 99.9% of speed of light = 0.999c

Mass of the Dave when moving at 99.9% of the speed of light:

$m=\frac{66 kg}{\sqrt{1-\frac{(0.999c)^2}{c^2}}}$

m = 1,467.17 kg

Mass of Dave when when moving at 99.9% of the speed of light is 1,467.17 kg.

4) Mass of the Dave = $m_o=66 kg$

Velocity of Dave,v=?

Mass of the Dave when moving at v speed of light: 500

$500 kg=\frac{66 kg}{\sqrt{1-\frac{(v)^2}{(3\times 10^8 m/s)^2}}}$

$v=2.973\times 10^8 m/s$

Dave should be moving at speed of $2.973\times 10^8 m/s$.