Q22P Question: A particle moves throu... [FREE SOLUTION]

91影视

Chapter 11: Q22P (page 322)

Question: A particle moves through an xyz coordinate system while a force acts on the particle. When the particle has the position vector $\overset{鈫�}{r} = (2.00 m) \hat{i} - (3.00 m) \hat{j} + (2.00 m) \hat{k}$ ,the force is given by $\overset{鈫�}{F} = F_{x} \hat{i} + (7.00 N) \hat{j} - (6.00 N) \hat{k}$ and the corresponding torque about the origin is $\overset{鈫�}{蟿} = (4.00 Nm) \hat{i} + (2.00 Nm) \hat{j} - (1.00 Nm) \hat{k}$ . Determine.

Short Answer

Expert verified

Answer

Force component along x-axis is- 5.00N

Step by step solution

Identification of given data

$\overset{鈫�}{r} = 2 \hat{i} - 3 \hat{j} + 2 \hat{k} \overset{鈫�}{F} = F_{x} \hat{i} + 7 \hat{j} - 6 \hat{k} \overset{鈫�}{蟿} = (4.0 Nm) \hat{i} + (2.0 Nm) \hat{j} - (1.00 Nm) \hat{k}$

To understand the concept

With the help of vector cross product, find the Force component along X-axis.

Write the equations for the cross product of radius vector and force and equate that cross product with the given torque. Now find the value of unknown component of the force.

Formulae:

$\overset{鈫�}{r} = x i + y j + z k \overset{鈫�}{F} = F_{x} i + F_{y} j + F_{z} k \overset{鈫�}{蟿} = \overset{鈫�}{r} 脳 \overset{鈫�}{F} = |\begin{matrix} i & j & k \\ x & y & z \\ F_{x} & F_{y} & F_{z} \end{matrix}| = (y F z - z F_{y}) \hat{i} + (z F_{x} - x F_{x}) \hat{j} + (x F_{y} - y F_{x}) \hat{k}$

Determine Fx

$\overset{鈫�}{蟿} = \overset{鈫�}{r} 脳 \overset{鈫�}{F} = |\begin{matrix} i & j & k \\ 2 & - 3 & 2 \\ F_{x} & 7 & - 6 \end{matrix}| = (18 - 14) \hat{i} + (2 F_{x} + 12) j \hat{} + (14 + 3 F_{x}) \hat{k} 鈬� \overset{鈫�}{蟿} = (4) \hat{i} + (2 F_{x} + 12) \hat{j} + (14 + 3 F_{x}) \hat{k}$

Now, this will compare with given torque vector.

$鈬� \overset{鈫�}{蟿} = (4.0 Nm) i + (2.0 Nm) j - (1.00 Nm) k$

Comparing,

$(2.0 Nm) j = (2 F_{x} + 12) j$

And,

$- (1.00 Nm) \hat{k} = (14 + 3 F_{x}) \tilde{k}$

Solving both of these two equations,

$F_{x} = - 5.00 N$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Identification of given data

To understand the concept

Determine Fx

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Classical Mechanics

Physical Quantities And Units

Dynamics

Work Energy and Power

Famous Physicists

Study anywhere. Anytime. Across all devices.