Explain how law of conservaton of energy holds true when a
roller coaster works
Answers
Explanation:
The law of conservation of energy states that “ Energy is neither created nor destroyed. But it can
be transformed from one from to another’’
Consider a body of mass ‘m’ sliding down a smooth inclined plane of angle q and vertical height h. At the highest point A the body has only potential energy. Since it is at rest, kinetic energy is zero.
Total energy at A,
= Potential Energy + Kinetic energy
= mgh………………(1)
Let the body slides down to a point D. Then it has both potential energy and kinetic energy.
Let ‘x’ be the vertical distance travelled by the body.
∴ Potential energy at D is =mg(h–x) its velocity at D is
v
2
=u
2
+2as
v
2
=0+2gsinθ. (AD)
(∵u=0,a=gsinθ,s=AD)
=2g
AD
x
∗AD
∵sinθ=
AD
x
,∵v
2
=2gx
Kinetic energy of the body
=
2
1
mv
2
=
2
1
m.(2gx)=mgx
Total energy at D is =mg(h−x)+mgx=mgh………….(2)
At the lowest point B, potential energy =0
Kinetic energy =
2
1
mv
2
=
2
1
m.(2gh)
∵v
2
=u
2
+2as=0+2gsinθ.(AB)
=2g∗AB=2gh,∵sinθ=
AB
h
Kinetic energy =mgh
∴ Total energy =0+mgh=mgh……………(3)
From (1), (2) and (3) it follows that total energy of the body remains constant while sliding down a inclined plane. Hence the