The series-200 train has one of the highest operating speed: 76.4 m/s. If a series-200 train has a maximum kinetic energy of 2.78 x 109 J, what is its mass?

Question

The series-200 train has one of the highest operating speed: 76.4 m/s.  If a series-200 train has a maximum kinetic energy of 2.78 x 10⁹ J, what is its mass?

Answer 1

KE = (1/2)mv² is the formula needed. Plug in the known values and solve for mass m.

 

2.78 x 10⁹ J = (1/2) m (76.4 m/s)²

 

m =  2.78 x 10⁹ / (1/2)(76.4)² = 9.53 x 10⁵ kg 

 

Answer 2

Tricia,

 

Kinetic Energy is given by:  K.E. = ½m·v² where m is the mass in kilograms, and v is the velocity in meters per second.  The unit of energy, the joule (J) is equivalent to kg·m²/s², so you're good to go, everything is already in the correct units.

 

 

Rearrange K.E. = ½m·v² to solve for m

 

m = 2(K.E.)/v²  ⇒ v² = 2·(2.78 x 10⁹ J)/(76.4 m/s)²

 

m = 9.5 x 10⁵ kg