The velocity ( v meters per second ) of a body is known to be proportional to the sqaure root of it's kinetic energy ( e ejoules). When the velocity of a body is 120m/s it's kinetic energy is 1600J.
Write down the relationship between v , e using k as the constant of varation.
Calculate the value of k
v = 21 , calculate the kenetic energy of the body in joules.
Can someone explain me please the right method in solving each quesion with the steps.
v= k sqrtKe
120=k sqrt 1600 solve for k, the proportionality constant.
Then,
v= k sqrt KE
ke= (v/k)^2
To solve each question, we need to use the relationship between velocity (v) and kinetic energy (e) that is given in the problem. Let's go through it step by step:
1. Write down the relationship between v and e using k as the constant of variation:
The problem states that the velocity of a body is proportional to the square root of its kinetic energy. We can express this using the equation: v ∝ √e. Here, ∝ indicates proportionality.
To remove the proportionality sign, we introduce a constant of variation, k. So, we can say v = k√e.
2. Calculate the value of k:
Given that when the velocity of a body is 120 m/s, its kinetic energy is 1600 J, we can plug these values into the equation v = k√e and solve for k.
Substituting v = 120 and e = 1600 into the equation, we get:
120 = k√1600.
To solve for k, divide both sides of the equation by √1600:
120/√1600 = k.
Simplifying the right side of the equation gives us:
k = 120/40.
So, the value of k is 3.
3. Calculate the kinetic energy (e) when the velocity (v) is 21 m/s:
Using the equation v = k√e, we can plug in the values of v = 21 and k = 3 to solve for e.
Rearranging the equation gives us e = (v/k)^2:
e = (21/3)^2.
Calculating the values inside the parentheses gives us:
e = 7^2.
Simplifying further results in:
e = 49 J.
Therefore, when the velocity is 21 m/s, the kinetic energy of the body is 49 J.