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Explanation:
The total mechanical energy of an object or system is given by:The total mechanical energy of an object or system is given by:
E
m
e
c
h
=
K
+
U
Where
K
is the kinetic energy of the object and
U
is the potential energy of the object. The carriage, sitting motionless at the top of the hill, has only potential energy in the form of gravitational potential energy.
Gravitational potential energy is given by:
U
g
=
m
g
h
Where
m
is the mass of the object,
g
is the gravitational acceleration constant, and
h
is the height of the object above some specific reference point, in this case the ground
21
m
below.
The weight of a stationary object at the surface of the earth is equal to the force of gravity acting on the object.
W
=
→
F
g
=
m
g
We are given that the carriage weighs
12
N
, therefore
m
g
=
12
N
.
U
g
=
12
N
⋅
21
m
⇒
U
g
=
252
N
m
=
252
J
E
m
e
c
h
=
K
+
U
Where
K
is the kinetic energy of the object and
U
is the potential energy of the object. The carriage, sitting motionless at the top of the hill, has only potential energy in the form of gravitational potential energy.
Gravitational potential energy is given by:
U
g
=
m
g
h
Where
m
is the mass of the object,
g
is the gravitational acceleration constant, and
h
is the height of the object above some specific reference point, in this case the ground
21
m
below.
The weight of a stationary object at the surface of the earth is equal to the force of gravity acting on the object.
W
=
→
F
g
=
m
g
We are given that the carriage weighs
12
N
, therefore
m
g
=
12
N
.
U
g
=
12
N
⋅
21
m
⇒
U
g
=
252
N
m
=
252
J