A 2.5 kg lead ball and a 55 g piece of lead shot are both dropped from a height of 25m. what is the kinetic energy of each object just before hitting the ground? What is the speed of each object just before hitting the ground
Answers
Answer:
Earth acceleration ~ 10 m/s^2
big mass = 2.5 kg; small mass =0.055 kg
drop of height = 25 m
Epot = m⋅g⋅h ; Ekin =1/2⋅m⋅v^2
The Epot is transformed into Ekin. Therefore: m⋅g⋅h = 1/2⋅m⋅v^2 (cancel m)
g⋅h = 1/2⋅v^2 ; solve for v: v = √(2⋅g⋅h); substitute the given dates:
v = √(2⋅10⋅25) = 22.36 also: hitting the ground at speed 22.36 m/s for the big and the small masses !
Ekinbig = 2.5⋅10⋅25 = 625; The big mass has an Ekin of 625 kgv^2
Ekinsmall = 0.055⋅10⋅25 = 13.75 ; The small mass has Ekin of 13.75 kgv^2
Remark: The check of the correct dimension is very easy to do. Just do not mixe numbers with dimensions, because it leads only to confusion. Do the calculations only with numbers !!! Add at the end the dimension necessary. It should not surprise you, that the speed of hitting the ground does not depend on the masses !!!
Explanation: