The kinetic Energy (K0 of a moving object varies jointly with its mass (m) and the square of its velocity (v). If an object has a mass of 22.5 kilograms and moving with a velocity of 20 meters per second has a kinetic energy of 4500 Joules, find
its kinetic energy when the velocity is
32 meters per second.
To find the kinetic energy when the velocity is 32 meters per second, we can use the joint variation equation:
K = k * m * v^2
Where K is the kinetic energy, m is the mass, v is the velocity, and k is the constant of variation.
We are given that when the object has a mass of 22.5 kilograms and is moving with a velocity of 20 meters per second, the kinetic energy is 4500 Joules. Let's use this information to find the value of k.
4500 = k * 22.5 * 20^2
First, let's calculate 20^2:
20^2 = 400
Now, substitute the values into the equation:
4500 = k * 22.5 * 400
To find k, divide both sides of the equation by (22.5 * 400):
k = 4500 / (22.5 * 400)
k = 0.5
Now that we have the value of k, we can find the kinetic energy when the velocity is 32 meters per second.
K = k * m * v^2
K = 0.5 * 22.5 * 32^2
First, calculate 32^2:
32^2 = 1024
Now substitute the values into the equation:
K = 0.5 * 22.5 * 1024
K = 11520 Joules
Therefore, when the velocity is 32 meters per second, the kinetic energy of the object is 11520 Joules.
To solve this problem, we need to use the relationship given between kinetic energy (K), mass (m), and velocity (v):
K = k * m * v^2
Where k is the constant of variation.
Given that the kinetic energy (K) is 4500 Joules when the mass (m) is 22.5 kilograms and the velocity (v) is 20 meters per second, we can substitute these values into the equation and solve for k:
4500 = k * 22.5 * 20^2
First, let's simplify the equation:
4500 = k * 22.5 * 400
Next, divide both sides of the equation by (22.5 * 400) to solve for k:
k = 4500 / (22.5 * 400)
k = 0.5
Now we have the value of k, which is 0.5. We can use this value to find the kinetic energy when the velocity is 32 meters per second.
To find the new kinetic energy (K1) when the velocity is 32 meters per second, we substitute the new velocity (v1 = 32) into the equation:
K1 = 0.5 * 22.5 * 32^2
Simplifying this equation:
K1 = 0.5 * 22.5 * 1024
K1 = 11520 Joules
Therefore, when the velocity is 32 meters per second, the object's kinetic energy is 11520 Joules.