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# What is the normal force on the object of mass m$_1$ (20 kg) shown in the diagram? What is the acceleration of the object?

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## 1 Answer

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Answer: 200 N and 1.572 m/s$^2$
Let us draw the Free body diagram for the problem stated.
Applying Newton's Second Law separately to the i and j components:
Along the y-axis, $F_y = ma_y \rightarrow N - m_1g - F_1 \sin 35 + F_2 \sin 43 = 0$
$\Rightarrow N = 20 \times 9.8 + 25 \sin 35 - 15 \sin 43 = 200.3\; N$
Along the x-axis, $F_x = ma_x \rightarrow F_1 \cos 35 + F_2 \cos 43 =m_1 a$
$\Rightarrow a = \large\frac{25 \cos 35 + 15 \cos 43}{20}$$= 1.572\;m/s^2$
answered Aug 19, 2014

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