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GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper
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© examsnet.com
Question : 43
Total: 65
A car having weight
W
is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height
h
from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is
I
. The acceleration of the car is
a
, and acceleration due to gravity is
g
.
The reactions on the front wheels
(
R
f
)
and rear wheels
(
R
r
)
are given by
R
f
=
R
r
=
W
2
+
W
g
(
h
I
)
a
R
f
=
W
2
+
W
g
(
h
l
)
a
;
R
r
=
W
2
−
W
g
(
h
l
)
a
R
t
=
W
2
−
W
g
(
h
l
)
a
;
R
r
=
W
2
+
W
g
(
h
l
)
a
R
t
=
R
r
=
W
2
−
W
g
(
h
l
)
a
Validate
Solution:
The car is moving in the forward direction, so the pseudo force will act in the backward direction
Taking moments about A and equating it to 0, we get
R
f
×
l
+
m
a
×
h
−
W
×
l
2
=
0
Where,
m
=
mass of the car
=
w
g
Substituting this in the above equation,
R
f
×
l
+
W
g
a
×
h
−
W
×
l
2
=
0
⇒
R
f
=
W
2
−
W
g
(
h
l
)
a
Similarly, if we take moment about point B and equate it to 0, we get
R
r
=
W
2
+
W
g
(
h
l
)
a
© examsnet.com
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