91影视

Consider a roller slides through a ramp of inclination angle ${15}^0$.

The force acting on the sliding surface of the roller is role="math" localid="1649685033863" $F_{x1}=12000N$

The force acting normal to the roller is role="math" localid="1649685039793" $F_{y1}=14500N$

The weight of the roller is $F_G=15000N$

Resolving forces in x-direction $\underset{x}{鈭�}F$

$F_x=12000N+F_G\sin \left({15}^0\right)=12000N+3882N=15882N$

Resolving forces in y-direction $\underset{y}{鈭�}F$

$F_y=F_y-F_G\cos \left({15}^0\right)=14500-14489N鈮�11N$

Resultant force F is given by

$F=\sqrt{{F^2}_x+{F^2}_y}=\sqrt{{15882}^2+{11}^2}=15882N$

To find the mass of the roller

$$\begin{gathered} F_G=mg \\ m=\frac{F_G}{g}=\frac{15000}{9.81}=1529kg \end{gathered}$$

To find the acceleration $a_x$of the roller

role="math" localid="1649689866017" $a_x=\frac{F_x}{m}=\frac{15882}{1529}=10.4m/s^2$

To find the velocity of the roller we have

$V_{1x}=V_{0x}+a_x鈭�t$where$V_{0x}=0and鈭�t=3sec.$

$鈭�V_{1x}=0+10.4\left(3\right)=31.2鈮�32m/s$

The velocity of the body is$32m/s$