6.
A. 1575 - 1265 = 310J
B. KE 1/2 MV^2
V=√2·KE/M = √2(310)/12 V = 7.2mls
C. PE = 1265 = mgh
h= 1265/mg = 1265/(12)(92) h= 10.8m
7.
A. KE = 1/2 mv^2 0.5(5)(12)^2 KE = 360J
B. PE = mgh = (5)(9.8)(2.6) PE = 127.4J
C. ME = KE + PE = 360 + 127.4 ME = 487.4J
Kinetic energy is the energy of a body due to the virtue of its motion while potential energy is the energy of a body due to the virtue of its position.
1a) The formula for calculating the mechanical energy of an object is expressed as:
[tex]ME = PE + KE[/tex]
Given the following parameters
P.E = 1265Joules
M.E = 1575Joules
Substitute the given parameters into the formula;
[tex]K.E=M.E-P.E\\K.E=1575-1265\\K.E=310Joules[/tex]
The kinetic energy of the body is 310 Joules
b) The formula for calculating the kinetic energy is expressed as:
[tex]K.E=\frac{1}{2}mv^2\\310=\frac{1}{2}(12)v^2\\620=12v^2\\v^2=\frac{620}{12} \\v^2= 51.66\\v=7.19m/s[/tex]
Hence if the mass of the object is 12 kg, the speed will be 7.19m/s
c) The formula for calculating the potential energy is expressed as:
[tex]P.E=mgh\\1265=12(9.8)h\\h=\frac{1265}{117.6}\\h= 10.76m[/tex]
Hence the height of the object is 10.76m
2a) Given the following parameters
Mass = 5kg
Speed = 12m/s
Height = 2.6m
[tex]K.E=0.5mv^2\\K.E=0.5(5)(12)^2\\K.E=360Joules[/tex]
b) Get the potential energy
Potential Energy = mgh
Potential Energy = 5 * 9.8 * 2.6
Potential Energy = 127.4joules
c) Mechanical energy = P.E + K.E
Mechanical energy = 360 + 127.4
Mechanical energy = 487.4Joules
Hence the mechanical energy of the body is 487.4Joules
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