91影视

• Mass of the body, $\mathrm{m}=1.0\mathrm{kg}$.
• Acceleration of the body, $\stackrel{鈬赌}{a}=2.0m/s^2$
• Angle of acceleration, $胃=20掳$.

Newton鈥檚 second law states that the net force on the body is the vector sum of all the forces acting on the body. The product of mass m and acceleration $\stackrel{\mathbf{鈫�}}{\mathbf{a}}$ of the body is equal to the net force ${\stackrel{\mathbf{鈫�}}{\mathit{F}}}_{Net}$ on the body. The relation is given by,

${\stackrel{\mathbf{鈫�}}{\mathbf{F}}}_{\mathbf{Net}}\mathbf{=}\mathit{m}\stackrel{\mathbf{鈫�}}{\mathbf{a}}$

Using the formula for Newton鈥檚 second law, we can find the x and y components of the net force and net force in unit-vector notation.

Formulae:

The net force on a particle according to Newton鈥檚 second law,

$$\begin{gathered} {\stackrel{鈫�}{F}}_{net}=F_1+F_2 \\ =M\stackrel{鈫�}{a} \end{gathered}$$ (i)

From equation (i), we get the x-component of force. Substitute the values of mass, and x component of acceleration in equation (i).

$\begin{array}{l}\stackrel{鈫�}{F}=Macos胃\\ =(1.00\mathrm{kg})(2.00{\mathrm{m}/\mathrm{s}}^2)cos\left({20}^0\right)\\ =1.88\mathrm{N}\end{array}$

Hence, the value of the x-component is $1.88\mathrm{N}$.

From equation (i), we get the y-component of force. Substitute the values of mass, and y component of acceleration in equation (i).

Hence, the value of y-component is $0.684\mathrm{N}$.

The net force is equal to the sum of its x and y components. Therefore, from part (a) and (b), we can write as,

$\begin{array}{lll}\stackrel{鈫�}{F}=F_x\hat{i}+F_y\hat{j}& & \\ =(1.88\mathrm{N})\hat{\mathrm{i}}+(0.684\mathrm{N})\hat{\mathrm{j}}& & \end{array}$

Hence, the force is $\left(1.88\mathrm{N}\right)\hat{i}+\left(0.684\mathrm{N}\right)\hat{j}$.