If vec{F} = (5 hat{i} - 10 hat{j}) text{ N} a | vedclass

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(B) The torque $\vec{	au}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{	au} = \vec{r} 	imes

Vedclass · Accepted Answer

$-25 \hat{k} 	ext{ N m}$

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(B) The torque $\vec{	au}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{	au} = \vec{r} 	imes \vec{F}$Given $\vec{r} = (4 \hat{i} - 3 \hat{j})$ and $\vec{F} = (5 \hat{i} - 10 \hat{j})$:$\vec{	au} = (4 \hat{i} - 3 \hat{j}) 	imes (5 \hat{i} - 10 \hat{j})$Using the distributive property of the cross product:$\vec{	au} = 4 \hat{i} 	imes (5 \hat{i}) - 4 \hat{i} 	imes (10 \hat{j}) - 3 \hat{j} 	imes (5 \hat{i}) + 3 \hat{j} 	imes (10 \hat{j})$Since $\hat{i} 	imes \hat{i} = 0$ and $\hat{j} 	imes \hat{j} = 0$,and knowing $\hat{i} 	imes \hat{j} = \hat{k}$ and $\hat{j} 	imes \hat{i} = -\hat{k}$:$\vec{	au} = 0 - 40(\hat{k}) - 15(-\hat{k}) + 0$$\vec{	au} = -40 \hat{k} + 15 \hat{k}$$\vec{	au} = -25 \hat{k} 	ext{ N m}$

If $\vec{F} = (5 \hat{i} - 10 \hat{j}) \text{ N}$ and $\vec{r} = (4 \hat{i} - 3 \hat{j}) \text{ m}$,then the torque $\vec{\tau}$ acting on the object will be:

Similar Questions

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