A. PE=360KJ KE=60KJ and v=10m/s
B. PE=180KJ KE=240KJ and v=20m/s
C. PE=0J KE=420KJ and v=26.46m/s
D. PE=120KJ KE=300KJ and v=22.36m/s
E. PE=240KJ KE=180KJ and v=17.32m/s
1. 360KJ.
2.12KW
3.The total energy is equal at every point, by conservation of energy.
4.Kinetic energy is greatest at point C, and so is velocity. It makes sense for KE to become greater as v becomes greater since the formula for KE shows that kinetic energy is a product of velocity and weight.
5. As PE lowers, KE grows and vice versa since due to the conservation of momentum, energy cant 'die' or disappear, it can only be changed into a new form of energy.
Step-by-step explanation:
First off: Potential energy=mgh, where m is mass, g is acceleration due to gravity and h is height. Kinetic energy=(1/2)mv², where m is mass again and v is velocity.
Let g=10m/s², let PE denote potential energy, let KE denote kinetic energy and let E denote total energy (PE+KE). Due to conversation of energy, the value of E will remain constant.
v, in terms of KE, is equal to √(2KE/m)
A
PE=mgh=(1200)(10)(30)=360,000J=360KJ
KE=(1/2)mv²=(1/2)(1200)(10²)=60,000J=60KJ
E=PE+KE=360,000+60,000=420,000J=420KJ
B
PE=mgh=(1200)(10)(15)=180,000J=180KJ
KE=E-PE=420,000-180,000=240,000J=240KJ
v=√(2KE/m)=√(2(240,000)/1,200)=√400=20m/s
C
PE=mgh=(1200)(10)(0)=0J
KE= E-PE = 420,000KJ=420KJ
v=√(2KE/m)=√(2(420,000)/1,200)=√700=26.4575131106≈26.46m/s
D
PE=mgh=(1200)(10)(10)=120,000J=120KJ
KE=E-PE=420,000-120,000=300,000J=300KJ
v=√(2KE/m)=√(2(300,000)/1,200)=√500=22.360679775=22.36m/s
E
PE=mgh=(1200)(10)(20)=240,000J=240KJ
KE=E-PE=420,000-240,000=180,000J=180KJ
v=√(2KE/m)=√(2(180,000)/1,200)=√300=17.3205080757=17.32m/s
1. The work done to go up to that point is equal to the potential energy at that point (force=mg, work=(force)(height), therefore work=mgh=PE). So the work done to get to A is the potential energy at A, which is 360KJ.
2.Power=work/time=360000/30=12000=12KW
3.The total energy is equal at every point, by conservation of energy.
4.Kinetic energy is greatest at point C, and so is velocity. It makes sense for KE to become greater as v becomes greater since the formula for KE shows that kinetic energy is a product of velocity and weight.
5. As PE lowers, KE grows and vice versa since due to the conservation of momentum, energy cant 'die' or disappear, it can only be changed into a new form of energy.
