Kinetic Energy and Momentum

Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. It is given by the equation:

Kinetic Energy (KE) = (1/2) * mass * velocity^2

Where mass is the mass of the object and velocity is its speed.

Momentum:
Momentum is a vector quantity that describes the motion of an object. It is given by the equation:

Momentum (p) = mass * velocity

Where mass is the mass of the object and velocity is its speed.

Given Information:
The kinetic energy of the body is 1000 J.

Decrease in Momentum:
The momentum of the body is decreased by 50%. This means the new momentum is 50% of the original momentum.

Let's assume the original momentum is p1 and the new momentum is p2.

p2 = p1 * 0.5

Relationship between Kinetic Energy and Momentum:
The kinetic energy of an object can be related to its momentum using the following equation:

Kinetic Energy (KE) = (p^2) / (2 * mass)

Where p is the momentum of the object and mass is its mass.

Calculating the new kinetic energy:
We can use the relationship between kinetic energy and momentum to calculate the new kinetic energy.

KE2 = (p2^2) / (2 * mass)

Substituting the value of p2:

KE2 = ((p1 * 0.5)^2) / (2 * mass)

Simplifying:

KE2 = (p1^2 * 0.25) / (2 * mass)

KE2 = (p1^2) / (8 * mass)

Inverse of Kinetic Energy:
To find the inverse of the kinetic energy, we can take the reciprocal of the new kinetic energy:

1/KE2 = (8 * mass) / (p1^2)

Therefore, 1/kinetic energy becomes (8 * mass) / (p1^2).

Explanation:
In this problem, the initial kinetic energy of the body is given as 1000 J. We are told that the momentum of the body decreases by 50%. Using the relationship between kinetic energy and momentum, we can calculate the new kinetic energy.

By substituting the value of the new momentum into the equation for kinetic energy, we find that the new kinetic energy is equal to (p1^2) / (8 * mass), where p1 is the initial momentum of the body. Taking the reciprocal of this expression gives us the inverse of the kinetic energy, which is (8 * mass) / (p1^2).

Therefore, the answer to the question "1/kinetic energy becomes?" is (8 * mass) / (p1^2).