Formulas converting Potential Energy to Kinetic Energy

1. The problem statement, all variables and given/known data

A 5kg ball (m), is to be dropped 1 meter (h) in a vacuum with no resistance in the earth’s gravity (g).

Use the speed and motion equations to show that its KE at impact is equivalent to its PE at its starting point.

2. Relevant equations

PE = mgh
KE= 1/2mv^2
S = vt + 1/2gt^2
S = vt

3. The attempt at a solution

Since h = 1
PE = mg

To calculate KE, we need to calculate the time taken to fall 1 meter and hence calculate the velocity.

h = 0 + 1/2gt^2
t^2 = 2/g

S = vt
v = h/t
therefore
v = √g/2
and
v^2 = g/2

KE = 1/2mv^2
KE = 1/2 x mg/2
KE = mg/4

I’ve now done this a few times and by the above calculations, the KE is 1/4 of the PE.

There has to be an error somewhere in my calculations, hopefully someone help enlighten me 🙂

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