Slowing down your exercise increases intensity.

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

3 years ago

Calculate the force of gravity between a 2.50 kg newborn baby and a 80.0 kg doctor standing 0.250 m away. G = 6.67 E -11 N*m2/kg

Alex787 [66]

Answer: 2.13 × 10⁻⁷ N

Explanation:

Gravitational force exists between any two bodies having mass.

Force of gravity is given by:

$F =G\frac{Mm}{r^2}$

It is given that, mass of newborn baby is M = 2.50 kg

Mass of the doctor, m = 80.0 kg

Distance between the two, r = 0.250 m

Gravitational constant, G = 6.67 × 10⁻¹¹ N m²/kg²

⇒F = (6.67 × 10⁻¹¹ N m²/kg² × 2.50 kg × 80.0 kg )÷ (0.250 m)² = 2.13 × 10⁻⁷ N

Thus, the force of gravity between new born baby and doctor is 2.13 × 10⁻⁷ N.

7 0

3 years ago

If a 4 engine jet accelerates down a runway at 8.7 m/s^2, Suppose now that all 4 engins are operational on the jet from the prev

soldi70 [24.7K]

Answer:

$5.22m/s^2$

Explanation:

One of the first propulsion characteristics given in the example is that all engines are equal.

In this way if we have 4 engines running at the same time, it means that its capacity is 100%.

Under this premise, if 100% is found, the Jet is capable of reaching a speed of 8.7m / s ^ 2.

However, the question is, what would happen if 2.4 "Engines" now work.

To do this then we make a simple equivalence,

If 4 engines is the equivalent of 100%, when would it be 2.4 engines?

$X = \frac{2.4 * 100\%} { 4 }= 60\%$

In this way it would mean that the body could be driven to 60% of its total.

So

$Speed_{Decreased} = 8.7 * 60\% = 5.22 \frac{m}{s^2}$

3 0

3 years ago

How can two machines appear identical and yet not have the same actual mechanical advantage

STatiana [176]

There are many factors which contributes as to how a machine will be processing the input energy and convert it to output energy. Even with identical mechanism, these factors will have major effect on the output. Some factors are deflection, friction and wear. Some system maybe exposed to poor lubrication than the other which'll produce more friction and wear thus lower mechanical advantage.

4 0

3 years ago

By the time she managed/had managed to open the door, the postman already went/had already gone.

leva [86]

Answer:

<h3>Answer Sentence: </h3><h2><em><u>By the time she had managed to open the door, the postman had already gone</u></em>.</h2>

8 0

3 years ago