Chapter 11: Q19P (page 322)

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 $\vec{F_{1}} = (3.0 N) \hat{k}$ and $\vec{F_{2}} = (- 2.0 N) \overset{\land}{J}$ act on the flea?

Short Answer

Expert verified

Net torque on flea is $- 2.0 \hat{i} N . m$

Step by step solution

Identification of given data

Position of flea is. $(0 m, - 4 m, 5 m)$

$F_{x} = 0 N, F_{y} = - 2.0 N, F_{z} = 3.0 N$

To understand the concept

Using the concept of torque, the unknown torque value is calculated. As per the concept, the torque acting on a body is due to the tangential force acting on a body along a radial path of the object in a circular motion. Thus, the cross-vector of the force and radial vector of the object will give the torque value.

Formulae:

The position vector in a 3-D diagram, $\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}$

The force vector in 3-D, $\vec{F} = F_{x} \hat{i} + F_{y} \hat{j} + F_{z} \hat{k}$

The torque acting on the body due to the tangential force, $\vec{τ} = \vec{r} \times \vec{F}$

Determining the net torque about the origin on the flea

We know that,
$\vec{τ} = \vec{r} \times \vec{F} = |\begin{matrix} i & j & k \\ x & y & z \\ F_{x} & F_{y} & F_{z} \end{matrix}| = (y F z - z F_{y}) \hat{i} + (z F_{x} - x F_{x}) \hat{j} + (x F_{y} - y F_{x}) \hat{k}$

After plugging the values, we get

$\begin{array}{rcl} \vec{τ} & = & \{(- 4 \times 3) N.m - (5 \times - 2) N.m\} \hat{i} + 0 N.m + 0 N.m \\ = & - 2.0 \hat{i} N.m \end{array}$

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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 $\vec{F_{1}} = (3.0 N) \hat{k}$ and $\vec{F_{2}} = (- 2.0 N) \overset{\land}{J}$ act on the flea?

Short Answer

Step by step solution

Identification of given data

To understand the concept

Determining the net torque about the origin on the flea

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In unit-vector notation, what is the net torque about the origin on a flea located at coordinates (0,-4.0m,5.0m)when forces F1→=(3.0N)k^and F2→=(-2.0N)J∧act on the flea?

Short Answer

Step by step solution

Identification of given data

To understand the concept

Determining the net torque about the origin on the flea

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Electricity

Work Energy and Power

Scientific Method Physics

Dynamics

Modern Physics

Study anywhere. Anytime. Across all devices.

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 $\vec{F_{1}} = (3.0 N) \hat{k}$ and $\vec{F_{2}} = (- 2.0 N) \overset{\land}{J}$ act on the flea?