I found the GPE using P=mgh and the KE using KE=1/2mv^2 but the GPE and the KE are coming out to be the same--is this correct or am I doing something wrong? I think I may be miscalculating the velocity for the KE.
{The problem is a 2.00 kg rock is dropped from rest at a height of 20m; ignore air resistance and determine the gravitational potential energy, kinetic energy, and total mechanical energy at the following heights: 20m, 10m, 0m}
{The problem is a 2.00 kg rock is dropped from rest at a height of 20m; ignore air resistance and determine the gravitational potential energy, kinetic energy, and total mechanical energy at the following heights: 20m, 10m, 0m}
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20 m:
GPE = mgh = 2*9.8*20 = 392 J
KE = ½mv² = ½*2*0² = 0 J
TME = GPE + KE = 392
10 m:
GPE = 2*9.8*10 = 196 J; V² = 2gy = 2*g*10 = 196 m²/s²
KE = ½m*V² = ½*2*196 = 196 J
TME = 392 J
0 m:
GPE = 2*g*0 = 0 J; V² = 2*g*20 = 392 m²/s²
KE = ½m*V² = 392 J
TME = 392 J
GPE = mgh = 2*9.8*20 = 392 J
KE = ½mv² = ½*2*0² = 0 J
TME = GPE + KE = 392
10 m:
GPE = 2*9.8*10 = 196 J; V² = 2gy = 2*g*10 = 196 m²/s²
KE = ½m*V² = ½*2*196 = 196 J
TME = 392 J
0 m:
GPE = 2*g*0 = 0 J; V² = 2*g*20 = 392 m²/s²
KE = ½m*V² = 392 J
TME = 392 J