Two forces (10+147) and (67 +107)
body is
act upon a body of mass 8 kg. Then the acceleration of the
11
Answers
Answer:
Given:
Two forces (10i + 14j) N and (6i + 10j) N act upon a body of mass 8 kg
To find:
Acceleration of the body.
Calculation:
Let net force be f.
\vec{f} = \{10 \hat{i} + 14 \hat{j} \} + \{6 \hat{i} + 10 \hat{j} \}
f
={10
i
^
+14
j
^
}+{6
i
^
+10
j
^
}
= > \vec{f} = \{16 \hat{i} + 24 \hat{j} \}=>
f
={16
i
^
+24
j
^
}
Acceleration is given as force/mass:
= > \vec{a} = \dfrac{ \{16 \hat{i} + 24 \hat{j} \} }{8}=>
a
=
8
{16
i
^
+24
j
^
}
= > \vec{a} = \{2 \hat{i} + 3 \hat{j} \}=>
a
={2
i
^
+3
j
^
}
Net magnitude of acceleration:
= > | \vec{a}| = \sqrt{ {(2)}^{2} + {(3)}^{2} }=>∣
a
∣=
(2)
2
+(3)
2
= > | \vec{a}| = \sqrt{ 4 + 9 }=>∣
a
∣=
4+9
= > | \vec{a}| = \sqrt{ 13} \: m {s}^{ - 2}=>∣
a
∣=
13
ms
−2
So , final answer is:
\boxed{ \blue{ \bold{ | \vec{a}| = \sqrt{ 13} \: m {s}^{ - 2} }}}
∣
a
∣=
13
ms
−2
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