Two balls of equal masses roll with velocities v and 4v,respectively .What is the ratio of their Kinetic Energies?
The kinetic energy of an object is given by the equation:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass, and v is the velocity.
Let's assume the mass of each ball is m.
For the first ball with a velocity v:
KE1 = (1/2) * m * v^2
For the second ball with a velocity 4v:
KE2 = (1/2) * m * (4v)^2
= (1/2) * m * 16v^2
= 8 * (1/2) * m * v^2
To find the ratio of their kinetic energies, we can divide KE2 by KE1:
KE2/KE1 = (8 * (1/2) * m * v^2) / ((1/2) * m * v^2)
Simplifying:
KE2/KE1 = 8
Therefore, the ratio of their kinetic energies is 8.
To find the ratio of the kinetic energies of two balls with equal masses but different velocities, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Let's assume the mass of each ball is m. Given that one ball has a velocity v and the other has a velocity 4v, we can calculate their kinetic energies.
For the ball with velocity v:
Kinetic Energy1 = (1/2) * m * v^2
For the ball with velocity 4v:
Kinetic Energy2 = (1/2) * m * (4v)^2 = (1/2) * m * 16v^2 = 8 * (1/2) * m * v^2 = 8 * Kinetic Energy1
So, the ratio of their kinetic energies is:
Kinetic Energy2 / Kinetic Energy1 = 8 * Kinetic Energy1 / Kinetic Energy1 = 8
Therefore, the ratio of their kinetic energies is 8:1.