Prove ∆Khj=∆Klj

Answer 1

To prove that ∆Khj = ∆Klj, we need to show that the change in kinetic energy for an object at points h and j is equal to the change in kinetic energy for the same object at points l and j.

The change in kinetic energy (∆K) can be calculated using the kinetic energy formula:

∆K = (1/2)mv^2

where m is the mass of the object and v is its velocity.

Since we are comparing the same object at different points, the mass (m) remains constant.

Thus, we can write the kinetic energy at point h as Kh = (1/2)m(vh^2) and the kinetic energy at point j as Kj = (1/2)m(vj^2).

The change in kinetic energy from point h to point j is then:

∆Khj = Kj - Kh
= (1/2)m(vj^2) - (1/2)m(vh^2)
= (1/2)m(vj^2 - vh^2)

Similarly, the kinetic energy at point l can be written as Kl = (1/2)m(vl^2).

The change in kinetic energy from point l to point j is:

∆Klj = Kj - Kl
= (1/2)m(vj^2) - (1/2)m(vl^2)
= (1/2)m(vj^2 - vl^2)

Since both expressions for ∆Khj and ∆Klj are (1/2)m multiplied by the difference of two velocity squares, we can conclude that ∆Khj = ∆Klj.