The bob of the pendulum is 200 g. It is swinging at a height of 1 m. The length of the pendulum is 1 m. Find the values of GPE, KE, and total mechanical energy at a height of 1 m, 0.5 m and 0.25 m and at its lowest point.
m=200g=0.2kgm = 200g = 0.2kgm=200g=0.2kg
g=9.8ms2g = 9.8\frac{m}{s^2}g=9.8s2m
E=GPE+KEE = GPE +KEE=GPE+KE
GPE=mghGPE = mghGPE=mgh
for h=1m\text{for }h=1mfor h=1m
KE=0KE = 0KE=0
GPE=0.2∗9.8∗1=1.96JGPE = 0.2*9.8*1= 1.96JGPE=0.2∗9.8∗1=1.96J
E=1.96JE = 1.96JE=1.96J
for h=0.5mE=1.96JGPE=0.2∗9.8∗0.5=0.98JKE=E−GPE=1.96−0.98=0.98J\text{for }h=0.5m\newline E = 1.96J\newline GPE = 0.2*9.8*0.5=0.98J\newline KE = E-GPE = 1.96-0.98 =0.98Jfor h=0.5mE=1.96JGPE=0.2∗9.8∗0.5=0.98JKE=E−GPE=1.96−0.98=0.98J
for h=0.25mE=1.96JGPE=0.2∗9.8∗0.25=0.49JKE=E−GPE=1.96−0.49=1.47J\text{for }h=0.25m\newline E = 1.96J\newline GPE = 0.2*9.8*0.25=0.49J\newline KE = E-GPE = 1.96-0.49 =1.47Jfor h=0.25mE=1.96JGPE=0.2∗9.8∗0.25=0.49JKE=E−GPE=1.96−0.49=1.47J
for h=0mE=1.96JGPE=0KE=E−GPE=1.96J\text{for }h=0m\newline E = 1.96J\newline GPE = 0\newline KE = E-GPE = 1.96Jfor h=0mE=1.96JGPE=0KE=E−GPE=1.96J
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