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4 years ago

6

Two equal forces are applied perpendicular to a door. The first force is applied at the midpoint of the door; the second force i

s applied at the doorknob. Which force exerts the greater torque?

1 answer:

Trava [24]4 years ago

5 0

Answer:

The second force at the doorknob

Explanation:

The magnitude of the torque is given by the following formula:

$\tau=rFsin\theta$

F is the applied force, r is the distance of the line of action of force from the axis of rotation and $\theta$ is the angle between them, in this case is $90^\circ$ for both points.

The door's midpoint it's half the distance from the doorknob. Thus, the torque at the doorknob is twice the torque at the door's midpoint.

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A commuter airplane starts from an airport and takes theroute. The plane first flies to city A, located 175 km away in a directi

bearhunter [10]

Answer:

245.45km in a direction 21.45° west of north from city A

Explanation:

Let's place the origin of a coordinate system at city A.

The final position of the airplane is given by:

rf = ra + rb + rc where ra, rb and rc are the vectors of the relative displacements the airplane has made. If we separate this equation into its x and y coordinates:

rfX = raX+ rbX + rcX = 175*cos(30)-150*sin(20)-190 = -89.75km

rfY = raY + rbY + rcT = 175*sin(30)+150*cos(20) = 228.45km

The module of this position is:

$rf = \sqrt{rfX^2+rfY^2} = 245.45km$

And the angle measure from the y-axis is:

$\alpha =atan(rfX/rfY) = 21.45\°$

So the answer is 245.45km in a direction 21.45° west of north from city A

6 0

4 years ago

A bicycle wheel of radius 0.28 m rolls down a hill without slipping. Its linear velocity increases constantly from 0 to 8 m/s in

Marina86 [1]

Answer:

10.989 rad/s²

Explanation:

Angular Acceleration: This is the acceleration of a body that undergoes a circular motion. The S.I unit of angular acceleration is rad/s²

The expression for angular acceleration is given as

a = αr.............. Equation 1

Where a = linear acceleration, α = angular acceleration, r = radius.

make α the subject of the equation

α = a/r............. Equation 2.

But,

a = (v-u)/t ............. Equation 3

Where v = final velocity, u = initial velocity, t = time.

substitute equation 3 into equation 2

α = (v-u)/rt............ Equation 4

Given: v = 8 m/s, u = 0 m/s, r = 0.28 m, t = 2.6 s

Substitute into equation 4

α = (8-0)/(0.28×2.6)

α = 8/0.728

α = 10.989 rad/s²

5 0

3 years ago

A block of gelatin is 120mm by 120mm by 40mm whrn unstressed. A force of 49N is applied tangentially to the upper surface causin

Inessa05 [86]

Answer:

The shearing stress is 10208.3333 Pa

The shearing strain is 0.25

The shear modulus is 40833.3332 Pa

Explanation:

Given:

Block of gelatin of 120 mm x 120 mm by 40 mm

F = force = 49 N

Displacement = 10 mm

Questions: Find the shear modulus, Sm = ?, shearing stress, Ss = ?, shearing strain, SS = ?

The shearing stress is defined as the force applied to the block over the projected area, first, it is necessary to calculate the area:

A = 40*120 = 4800 mm² = 0.0048 m²

The shearing stress:

$Ss=\frac{F}{A} =\frac{49}{0.0048} =10208.3333Pa$

The shearing strain is defined as the tangent of the displacement that the block over its length:

$SS=tan\theta =\frac{Displacement}{L} =\frac{10}{40} =0.25$

Finally, the shear modulus is the division of the shearing stress over the shearing strain:

$Sm=\frac{10208.3333}{0.25} =40833.3332Pa$

6 0

4 years ago

A convex mirror of focal length 34 cm forms an image of a soda bottle at a distance of 18 cm behind the mirror. The height of th

Mademuasel [1]

<h2>Answers:</h2>

In convex mirrors the focus is virtual and the focal distance is negative. This is how the reflected rays diverge and only their extensions are cut at a point on the main axis, resulting in a virtual image of the real object .

<h2 /><h2>a) Position of the soda bottle (the object) </h2><h2 />

The Mirror equation is:

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$ (1)

Where:

$f$ is the focal distance

$u$ is the distance between the object and the mirror

$v$ is the distance between the image and the mirror

We already know the values of $f$ and $v$ , let's find $u$ from (1):

$u=\frac{v.f}{v-f}$ (2)

Taking into account the explanation at the beginign of this asnswer:

$f=-34cm$ and $v=-18cm$

The <u>negative signs</u> indicate the <u>focal distance</u> and the <u>distance between the image and the mirror are virtual </u>

Then:

$u=\frac{(-18cm)(-34cm)}{-18cm-(-34cm)}$

$u=38.25cm$ (3) >>>>Position of the soda bottle

<h2>b) magnification of the image </h2><h2 />

The magnification $m$ of the image is given by:

$m=-\frac{v}{u}$ (4)

$m=-\frac{(-18cm)}{38.25cm}$

$m=0.47$ (5)>>>the image is 0.47 smaller than the object

<h2>The fact that this value is positive means the image is upright </h2>

<h2>c) Describe the image </h2><h2 />

According to the explanations and results obtained in the prior answers, the correct option is 9:

<h2>The image is <u>virtual, upright, smaller</u> than the object </h2><h2 /><h2>d) Height of the soda bottle (object) </h2>

Another way to find the magnification is by the following formula:

$m=\frac{h_{i}}{h_{o}}$ (6)

Where:

$h_{i}$ is the image height

$h_{o}$ is the object height

We already know the values of $m$ and $h_{i}$ , let's find $h_{o}$ :

$h_{o}=\frac{h_{i}}{m}$ (7)

$h_{o}=\frac{6.8cm}{0.47}$

$h_{o}=14.46cm$ (8) >>>height of thesoda bottle

6 0

3 years ago

An ice sheet 5m thick covers a lake that is 20m deep. what is the temperature of the water at the bottom of the lake? explain yo

umka2103 [35]

Answer:

4°C

Explanation:

Water is densest at 4°C. Since dense water sinks, the bottom of the lake will be 4°C.

5 0

3 years ago

Read 2 more answers