How much force is needed to pull a spring with a spring constant of 20 N/m a distance of<br> 25 m?

An overhead door is guided by wheels at a and b that roll in horizontal and vertical tracks. when θ = 40°, the velocity of wheel

Karo-lina-s [1.5K]

I think the situation is modeled by the scenario in the attached image. Some specific values seem to be missing (like the height of door $d$ )...

The door forms a right triangles that satisfies

$\tan\theta=\dfrac ab\implies\sec^2\theta\dfrac{\mathrm d\theta}{\mathrm dt}=\dfrac{b\frac{\mathrm da}{\mathrm dt}-a\frac{\mathrm db}{\mathrm dt}}{b^2}$

We also have

$\tan\theta=\dfrac ab\implies\cos\theta=\dfrac bd$

so if you happen to know the height of the door, you can solve for $b$ and $a$ .

$d$ is fixed, so

$a^2+b^2=d^2\implies2a\dfrac{\mathrm da}{\mathrm dt}+2b\dfrac{\mathrm db}{\mathrm dt}=0\implies\dfrac{\mathrm da}{\mathrm dt}=-\dfrac ba\dfrac{\mathrm db}{\mathrm dt}$

We can solve for the angular velocity $\dfrac{\mathrm d\theta}{\mathrm dt}$ :

$\dfrac{\mathrm d\theta}{\mathrm dt}=\cos^2\theta\dfrac{b\left(-\frac ba\frac{\mathrm db}{\mathrm dt}\right)-a\frac{\mathrm db}{\mathrm dt}}{b^2}=-\dfrac1a\dfrac{\mathrm db}{\mathrm dt}$

At the point when $\theta=40^\circ$ and $\dfrac{\mathrm db}{\mathrm dt}=1.8$ ft/s, we get

$\dfrac{\mathrm d\theta}{\mathrm dt}=-\dfrac{1.8}a\dfrac{\rm deg}{\rm s}=-\dfrac{1.8}{d\sin40^\circ}\dfrac{\rm deg}{\rm s}$

6 0

2 years ago

How many of each component are shown in the diagram? Check all that apply.

g100num [7]

Can you show the diagram please

3 0

2 years ago

What type of interaction allows the sidewalk to heat up and cook the egg?

Bogdan [553]

Answer:

Adsorption

Explanation:

Sidewalk cooking of egg is very popular in America. In summer people release fireworks in night sky and cook egg on the concrete sidewalk to check the level of temperature. When sunlight fall on the sidewalk most of the light is reflected back but some darker material adsorbs some photon, and when these photons are transferred to egg molecules it causes vibration among them and produce heat and cook egg.

7 0

2 years ago

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When you stop at a railroad crossing at night, instead of correctly perceiving two red lights that flash alternately you may per

Nezavi [6.7K]

I'm pretty sure that there should be an options to choose. Anyway, I've seen this question before and I know that this is an example of <span>the phi phenomenon.</span>

7 0

3 years ago

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when an object falls, eventually the force of air resistance (drag) = the force of gravity. This is called ____

jarptica [38.1K]

Terminal velocity dkdkmfocmdpdmfpfmfl

4 0

2 years ago

How much force is needed to pull a spring with a spring constant of 20 N/m a distance of 25 m?