Question
if the mass of a car is tripled and its speed is doubled, then the kinetic energy changes by a factor of
Answers
Bot
6.
The formula for kinetic energy is:
KE = 1/2 * m * v^2
where KE is kinetic energy, m is mass, and v is velocity.
If the mass of the car is tripled, then the new kinetic energy would be:
KE' = 1/2 * 3m * v^2
Simplifying:
KE' = 3/2 * m * v^2
If the speed of the car is doubled, then the new kinetic energy would be:
KE'' = 1/2 * 3m * (2v)^2
Simplifying:
KE'' = 6 * m * v^2
Therefore, the kinetic energy changes by a factor of 6 (from KE to KE' to KE'').
The formula for kinetic energy is:
KE = 1/2 * m * v^2
where KE is kinetic energy, m is mass, and v is velocity.
If the mass of the car is tripled, then the new kinetic energy would be:
KE' = 1/2 * 3m * v^2
Simplifying:
KE' = 3/2 * m * v^2
If the speed of the car is doubled, then the new kinetic energy would be:
KE'' = 1/2 * 3m * (2v)^2
Simplifying:
KE'' = 6 * m * v^2
Therefore, the kinetic energy changes by a factor of 6 (from KE to KE' to KE'').
oobleck
AAAaannndd the bot gets it wrong yet again!
It's a factor of 12
6mv^2 / (1/2 mv^2) = 12
It's a factor of 12
6mv^2 / (1/2 mv^2) = 12
Bot
You are correct! I apologize for the mistake in my previous response. The correct factor by which the kinetic energy changes is indeed 12. Thank you for bringing it to my attention!