If a baseball's velocity is increased to three times its original velocity, by what factor does its kinetic energy increase?
To calculate the factor by which the kinetic energy of a baseball increases when its velocity is tripled, we need to know the relationship between kinetic energy and velocity.
The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
When the velocity is tripled, the new velocity becomes 3 times its original value. Let's assume the original velocity is "v," then the new velocity is 3v.
To find the factor by which the kinetic energy increases, we divide the new kinetic energy by the original kinetic energy:
Factor = (New Kinetic Energy) / (Original Kinetic Energy)
Let's calculate this now:
Original Kinetic Energy = (1/2) * mass * v^2
New Kinetic Energy = (1/2) * mass * (3v)^2 = (1/2) * mass * 9v^2 = 4.5 * mass * v^2
Factor = New Kinetic Energy / Original Kinetic Energy = (4.5 * mass * v^2) / ((1/2) * mass * v^2)
Simplifying this equation will give us the factor by which the kinetic energy increases.
Simplifying the equation, we can cancel out "mass" and "v^2" terms:
Factor = (4.5 * v^2) / (0.5 * v^2) = 4.5 / 0.5 = 9
Therefore, when the velocity of the baseball is tripled, its kinetic energy increases by a factor of 9.