91影视

The acceleration is due to the gravitational acceleration's sin component when an object comes downward on an inclined plane in the absence of friction.

Given data:

The mass of the block is $m=7.0\mathrm{kg}$.

The angle of incline is $胃=22.0掳$.

The initial speed of the block along the x-axis is $v_{\mathrm{i}}=0$.

The distance of the block from the bottom is $螖x=12.0\mathrm{m}$.

Assumption:

Let a be the acceleration of the block.

Let the speed of the block be $v_{\mathrm{f}}$at the bottom of the incline along the x-axis.

Part (a)

The normal force acting on the block is $N=mg\cos 胃$.

The net force on the block is $F=mg\sin 胃$.

Then, the acceleration of the block is

$\begin{array}{c}a=\frac{mg\sin 胃}{m}\\ =g\sin 胃\\ =9.80\frac{\mathrm{m}}{{\mathrm{s}}^2}脳\sin 22.0^o\\ =3.67\frac{\mathrm{m}}{{\mathrm{s}}^2}\end{array}$

Hence, the acceleration of the block is $3.67\frac{\mathrm{m}}{{\mathrm{s}}^2}$.

Part (b)

Now, to find the final speed of the block at the bottom,

$\begin{array}{c}{v}_{\mathrm{f}}^2=v_{\mathrm{i}}^2+2a螖x\\ v_{\mathrm{f}}^2=0^2+2脳3.67\frac{\mathrm{m}}{{\mathrm{s}}^2}脳12\mathrm{m}\\ v_{\mathrm{f}}=9.39\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

Hence, the speed of the block is $9.39\frac{\mathrm{m}}{\mathrm{s}}$at the bottom of the incline.