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Two transmission belts pass over a double-sheaved pulley that is attachedto an axle supported by bearings at $A$ and $D$. The radius of the innersheave is $125 \mathrm{mm}$ and the radius of the outer sheave is $250 \mathrm{mm}$. Knowing that when the system is at rest, the tension is $90 \mathrm{N}$ in both portions of belt $B$ and $150 \mathrm{N}$ in both portions of belt $C$, determine the reactions at $A$ and $D .$ Assume that the bearing at $D$ does not exert any axial thrust.
State Newton's Second Law of Motion in vector form.
Consider the following position functions.a. Find the velocity and speed of the object.b. Find the acceleration of the object.$$\mathbf{r}(t)=\langle 13 \cos 2 t, 12 \sin 2 t, 5 \sin 2 t\rangle, \text { for } 0 \leq t \leq \pi$$
Consider the following position functions $\mathbf{r}$ and $\mathbf{R}$ for two objects.a. Find the interval $[c, d]$ over which the R trajectory is the same as the r trajectory over $[a, b]$b. Find the velocity for both objects.c. Graph the speed of the two objects over the intervals $[a, b]$ and $[c, d],$ respectively.$$\begin{aligned}&\mathbf{r}(t)=\left\langle t, t^{2}\right\rangle,[a, b]=[0,2]\\&\mathbf{R}(t)=\left\langle 2 t, 4 t^{2}\right\rangle \text { on }[c, d]\end{aligned}$$
Consider the following position functions $\mathbf{r}$ and $\mathbf{R}$ for two objects.a. Find the interval $[c, d]$ over which the R trajectory is the same as the r trajectory over $[a, b]$b. Find the velocity for both objects.c. Graph the speed of the two objects over the intervals $[a, b]$ and $[c, d],$ respectively.$$\begin{array}{l}\mathbf{r}(t)=\langle 1+3 t, 2+4 t\rangle,[a, b]=[0,6] \\\mathbf{R}(t)=\langle 1+9 t, 2+12 t\rangle \text { on }[c, d]\end{array}$$
Consider the following position functions $\mathbf{r}$ and $\mathbf{R}$ for two objects.a. Find the interval $[c, d]$ over which the R trajectory is the same as the r trajectory over $[a, b]$b. Find the velocity for both objects.c. Graph the speed of the two objects over the intervals $[a, b]$ and $[c, d],$ respectively.$$\begin{array}{l}\mathbf{r}(t)=\langle\cos t, 4 \sin t\rangle,[a, b]=[0,2 \pi] \\\mathbf{R}(t)=\langle\cos 3 t, 4 \sin 3 t\rangle \text { on }[c, d]\end{array}$$
