?Force \(\vec{F}=(-8.0 \mathrm{N}) \hat{i}+(6.0 \mathrm{N}) \hat{j}\) acts on a particle

In unit-vector notation, what is the net torque about the origin on a flea located at coordinates (0, ?4.0 m, 5.0 m) when forces \(\vec{F}_{1}=(3.0 \mathrm{N}) \hat{\mathrm{k}}\) and \(\vec{F}_{2}=(-2.0 \mathrm{N}) \hat{\mathrm{j}}\) act on the flea? Text Transcription: vec F_1 =(3.0N) hat k vec F_2=(-2.0N) hat j

A plum is located at coordinates (?2.0 m, 0, 4.0 m). In unit-vector notation, what is the torque about the origin on the plum if that torque is due to a force \(\vec{F}\) whose only component is (a) \(F_{x}=6.0 \mathrm{N}\), (b) \(F_{x}=-6.0 \mathrm{N}\), (c) \(F_{z}=6.0 \mathrm{N}\), and (d) \(F_{z}=-6.0 \mathrm{N}\)? Text Transcription: vec F F_x =6.0N F_x =-6.0N F_z =6.0N F_z =-6.0N

In unit-vector notation, what is the torque about the origin on a particle located at coordinates (0, ?4.0 m, 3.0 m) if that torque is due to (a) force \(\vec{F}_{1}\) with components \(F_{1 x}=2.0 \mathrm{N}, F_{1 y}=F_{1 z}=0\), and (b) force \(\vec{F}_{2}\) with components \(F_{2 x}=0, F_{2 y}=2.0 \mathrm{N}, F_{2 z}=4.0 \mathrm{N}\)? Text Transcription: vec F_1 F_1x =2.0N, F_1y =F_{1z=0 vec F_2 F_2x =0, F_2y =2.0N, F_2z =4.0N

A particle moves through an xyz coordinate system while a force acts on the particle. When the particle has the position vector \(\vec{r}=(2.00 \mathrm{m}) \hat{\mathrm{i}}-(3.00 \mathrm{m}) \hat{\mathrm{j}}+(2.00 \mathrm{m}) \hat{\mathrm{k}}\), the force is given by \(\vec{F}=F_{x} \hat{i}+(7.00 \mathrm{N}) \hat{j}-(6.00 \mathrm{N}) \hat{k}\) and the corresponding torque about the origin is \(\vec{\tau}=(4.00 \mathrm{N} \cdot \mathrm{m}) \hat{\mathrm{i}}+(2.00 \mathrm{N} \cdot \mathrm{m}) \hat{\mathrm{j}}-(1.00 \mathrm{N} \cdot \mathrm{m}) \hat{\mathrm{k}}\). Determine \(F_{x}\). Text Transcription: vec r =(2.00m) hat i -(3.00m) hat j +(2.00m) hat k vec F =F_x hat i +(7.00N) hat j -(6.00N) hat k vec tau =(4.00N cdot m) hat i +(2.00N cdot m F_x

Force \(\vec{F}=(2.0 \mathrm{N}) \hat{\mathrm{i}}-(3.0 \mathrm{N}) \hat{\mathrm{k}}\) acts on a pebble with position vector \(\vec{r}=(0.50 \mathrm{m}) \hat{\mathrm{j}}-(2.0 \mathrm{m}) \hat{\mathrm{k}}\) relative to the origin. In unit-vector notation, what is the resulting torque on the pebble about (a) the origin and (b) the point (2.0 m, 0, ?3.0 m)? Text Transcription: vec F=(2.0N) hat i -(3.0N) hat k vec r=(0.50m) hat j -(2.0m) hat k

In unit-vector notation, what is the torque about the origin on a jar of jalapeño peppers located at coordinates (3.0 m, ?2.0 m, 4.0 m) due to (a) force \(\vec{F}_{1}=(3.0 \mathrm{N}) \hat{\mathrm{i}}-(4.0 \mathrm{N}) \hat{\mathrm{j}}+(5.0 \mathrm{N}) \hat{\mathrm{k}}\), (b) force \(\vec{F}_{2}=(-3.0 \mathrm{N}) \hat{i}-(4.0 \mathrm{N}) \hat{\mathrm{j}}-(5.0 \mathrm{N}) \hat{\mathrm{k}}\), and (c) the vector sum of \(\vec{F}_{1}\) and \(vec{F}_{2}\)? (d) Repeat part (c) for the torque about the point with coordinates (3.0 m, 2.0 m, 4.0 m). Text Transcription: vec F_1 =(3.0N) hat i -(4.0N) hat j +(5.0N) hat k vec F_2 =(-3.0N) hat i -(4.0N) hat j -(5.0N) hat k vec F_1 vec F_2

Force \(\vec{F}=(-8.0 \mathrm{N}) \hat{i}+(6.0 \mathrm{N}) \hat{j}\) acts on a particle with position vector \(\vec{r}=(3.0 \mathrm{m}) \hat{\mathrm{i}}+(4.0 \mathrm{m}) \hat{\mathrm{j}}\). What are (a) the torque on the particle about the origin, in unit-vector notation, and (b) the angle between the directions of \(\vec{r}\) and \(\vec{F}\)? Text Transcription: vec F=(-8.0N) hat i +(6.0N) hat j vec r=(3.0m) hat i +(4.0m) hat j vec r vec F