The relationship between momentum (p) and kinetic energy (KE) can be expressed as:
KE = (p^2) / (2m)
where p is the momentum of the body and m is its mass.
To determine the percentage increase in kinetic energy, we'll compare the initial kinetic energy (KE1) to the final kinetic energy (KE2) after the momentum is increased by 10%.
Let's assume the initial momentum is p1, and the final momentum is p2, such that p2 = 1.1 * p1.
To find the initial kinetic energy, we substitute p1 into the kinetic energy formula:
KE1 = (p1^2) / (2m)
Similarly, we can find the final kinetic energy using p2:
KE2 = (p2^2) / (2m) = (1.1 * p1)^2 / (2m)
Now, let's calculate the percentage increase in kinetic energy:
% Increase in KE = ((KE2 - KE1) / KE1) * 100
Substituting the values, we get:
% Increase in KE = (((1.1 * p1)^2 / (2m)) - ((p1^2) / (2m))) / ((p1^2) / (2m)) * 100
Simplifying the equation:
% Increase in KE = (((1.21 * p1^2) - p1^2) / (p1^2)) * 100
% Increase in KE = (0.21 * p1^2 / p1^2) * 100
% Increase in KE = 0.21 * 100
% Increase in KE = 21%
Therefore, the percentage increase in kinetic energy of the body is 21% when its momentum is increased by 10%.
Answers & Comments
Answer:
The relationship between momentum (p) and kinetic energy (KE) can be expressed as:
KE = (p^2) / (2m)
where p is the momentum of the body and m is its mass.
To determine the percentage increase in kinetic energy, we'll compare the initial kinetic energy (KE1) to the final kinetic energy (KE2) after the momentum is increased by 10%.
Let's assume the initial momentum is p1, and the final momentum is p2, such that p2 = 1.1 * p1.
To find the initial kinetic energy, we substitute p1 into the kinetic energy formula:
KE1 = (p1^2) / (2m)
Similarly, we can find the final kinetic energy using p2:
KE2 = (p2^2) / (2m) = (1.1 * p1)^2 / (2m)
Now, let's calculate the percentage increase in kinetic energy:
% Increase in KE = ((KE2 - KE1) / KE1) * 100
Substituting the values, we get:
% Increase in KE = (((1.1 * p1)^2 / (2m)) - ((p1^2) / (2m))) / ((p1^2) / (2m)) * 100
Simplifying the equation:
% Increase in KE = (((1.21 * p1^2) - p1^2) / (p1^2)) * 100
% Increase in KE = (0.21 * p1^2 / p1^2) * 100
% Increase in KE = 0.21 * 100
% Increase in KE = 21%
Therefore, the percentage increase in kinetic energy of the body is 21% when its momentum is increased by 10%.