Object A has mass m and velocity v. Object B has 18 times the mass and one third the velocity of object A.
The kinetic energy of object B will be Spell check times the kinetic energy of object A.
A
(1/2) m v^2
B
(1/2)(18m)v^2/9
B/A = twice
To find the kinetic energy of an object, we use the formula:
Kinetic Energy = 1/2 * mass * velocity^2
Let's calculate the kinetic energy of object A:
Kinetic Energy of object A = 1/2 * m * v^2
Now, let's calculate the kinetic energy of object B:
Mass of object B = 18 times the mass of object A = 18m
Velocity of object B = one third the velocity of object A = v/3
Kinetic Energy of object B = 1/2 * (18m) * (v/3)^2
= 1/2 * 18m * (v^2/9)
= 9 * m * (v^2/9)
= m * v^2
Therefore, the kinetic energy of object B will be equal to the kinetic energy of object A, as the extra factor of "9" cancels out:
Kinetic Energy of object B = Kinetic Energy of object A
To determine the kinetic energy of two objects, you need to use the formula:
Kinetic energy = (1/2) * mass * velocity^2
Let's find the kinetic energy of object A first. Given that object A has mass m and velocity v, its kinetic energy will be:
KE_A = (1/2) * m * v^2
Next, let's find the kinetic energy of object B. According to the given information, object B has 18 times the mass of object A and one-third the velocity of object A. Therefore:
Mass of B = 18m
Velocity of B = (1/3)v
Now we can calculate the kinetic energy of object B:
KE_B = (1/2) * (18m) * [(1/3)v]^2
= (1/2) * 18m * (1/9) * v^2
= (9/2) * m * v^2
Now we can compare the kinetic energy of object B to object A:
KE_B / KE_A = [(9/2) * m * v^2] / [(1/2) * m * v^2]
= (9/2) / (1/2)
= 9 * 2
= 18
Therefore, the kinetic energy of object B is 18 times the kinetic energy of object A.