When a certain force is applied to an object with a mass of 2 kg, its acceleration is 10.0 m/s^2. When the same force is applied to a different object, its acceleration is 4.0 m/s^2. What is the mass of the second object?
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The “certain force” denoted F is assumed to be the net force on the object when it gives m1 an acceleration a
1
=12m/s
2
and when it gives m2 an acceleration a
2
=3.3m/s
2
. Thus, we substitute m
1
=F/a
1
and m
2
=F/a
2
in appropriate places during the following manipulations.
(a) Now we seek the acceleration a of an object of mass m
2
−m
1
when F is the net force on it. Thus,
a=
m
2
−m
1
F
=
(F/a
2
)−(F/a
1
)
F
=
a
1
−a
2
a
1
a
2
which yields a=4.6m/s
2
.
(b) Similarly for an object of mass m
2
+m
1
:
a=
m
2
+m
1
F
=
(F/a
2
)+(F/a
1
)
F
=
a
1
+a
2
a
1
a
2
which yields a=2.6m/s
2
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