1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sladkih [1.3K]
3 years ago
11

A wrench 0.1 meters long lies along the positive yy-axis, and grips a bolt at the origin. A force is applied in the direction of

⟨0,2,−4⟩⟨0,2,−4⟩ at the end of the wrench. Find the magnitude of the force in Newtons needed to supply 100 Newton-Meters of torque to the bolt.
Mathematics
1 answer:
Gemiola [76]3 years ago
8 0

Answer:

Therefore the magnitude of the applied force is 500\sqrt 5 N.

Step-by-step explanation:

Torque: Torque is the cross product of force and the distance of applied force  from the rotational axis.

\tau=\vec  F\times \vec r= |F||r| sin\theta

Where \theta is angle between F and r.

Newton-meter is the S.I unit of torque.

Along the positive y axis, the wrench lies .

The length of wrench is 0.1 m.

\vec r= 0.1 \hat j   [ since the vector \vec r lies on y axis]

The direction of applied force is along the vector <0,2,-4>.

Then the angle between \vec r and <0,2,-4> = the angle between F and \vec r.

We know that,

\vec a.\vec b=|\vec a||\vec b|cos \theta

\vec r .  =(0.1 \hat j) .(0\hat i+2 \hat j -4\hat k) =0+(0.1).2+0.(-4)=0.2

|\vec r|.|| cos \theta= \sqrt{0.1^2}.\sqrt{0^2+2^2+(-4)^2} \  cos \theta

\therefore\sqrt{(0.1)^2}.\sqrt{0^2+2^2+(-4)^2} \  cos \theta= 0.2

\Rightarrow (0.1).2\sqrt5 cos \theta =0.2

\Rightarrow  cos \theta =\frac{0.2}{0.2\sqrt 5}

\Rightarrow  cos \theta =\frac{1}{\sqrt 5}

We know that,

sin \theta =\sqrt{1-cos^2\theta}=\sqrt{1-(\frac{1}{\sqrt5})^2}

                            =\sqrt {1-\frac15}

                            =\sqrt {\frac{5-1}{5}

                            =\frac{2}{\sqrt 5}

Here \tau = 100 N-m, \vec r=0.1 \hat j and sin \theta = \frac{2}{\sqrt 5}

Now

\tau=|F||r| sin\theta

\Rightarrow 100= |F|(0.1) \frac{2}{\sqrt 5}

\Rightarrow |F|=\frac{100\times \sqrt5}{0.2}

\Rightarrow |F|=500\sqrt 5

Therefore the magnitude of the force is 500\sqrt 5 N.

                               

You might be interested in
Please help, thanks!<br><br> Factor completely<br><br> Sx²- 13x² + 15x²
Andru [333]

Answer:

x^2(S+2)

Step-by-step explanation:

7 0
3 years ago
In 3/4 pound of a spice mix there is 5/6 cup of cinnamon how much is it if it is a spice mix contain per pound?
nordsb [41]

There are 10/9 cups of cinnamon in 1 pound of spice mix

and if you wanna convert the improper fraction to a mixed number it will be 11/9

5 0
2 years ago
660 ft per minute = ____ ft per second
Klio2033 [76]
The answer might be 39,600
6 0
3 years ago
Read 2 more answers
PEASE HELP ASAP!!! The sum of two numbers is 58.
agasfer [191]

Answer:

y=15

x=43

(any variable can be used, I used x and y to make it easier to show)

Step-by-step explanation:

x+y=58

x-y=28

get x by its self

x=58-y

then subsitute into the other equation

(58-y)-y=28

58-2y=28

-2y=-30

y=15

sub. again

x+15=58

x=43

8 0
2 years ago
Read 2 more answers
FRER POINTS ANSWR NOW........
Alika [10]

Answer:

Hey I’m early and actually get points

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches and a standard devia
    13·1 answer
  • Ram wants to work to preserve marine habitats. Which field of study would be most useful to him
    5·2 answers
  • What is y equals one third times two plus four
    11·2 answers
  • A girl scout troop sold cookies. If the girls Sold 5 more boxes the second week than they did the first and if they doubled the
    7·1 answer
  • To 6x - 5(2x - 4) = 3x - 6?
    5·1 answer
  • Acording to what the harder you pedal a bicycle thr faster it will go
    7·2 answers
  • Find the inverse of each given functions h(x)=2x-4/3
    15·2 answers
  • What is the NOT A RESTRICTION on the quotient of quantity 5 x squared minus 10 x minus 15 divided by quantity x squared minus 9
    9·1 answer
  • Simplify -2/3 + -4/5 + 7/15 + -11/20
    11·1 answer
  • Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. She wants to leave 16% of the total bill
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!