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Tasya [4]
3 years ago
15

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

b is 1.8 ft/s upward. determine the angular velocity of the door and the velocity of end d of the door.

Physics
1 answer:
Karo-lina-s [1.5K]3 years ago
6 0

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}

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Answer:

See Below

Explanation:

Okay, I thinkkk what it is asking by what you summarzied for me issss:

They split the total time into four quarters. They then took (for the first quarter) the start time. Then when the first quarter ends and the second quarter starts is the "end" time.

They then subtract the start time of the second quarter from the end time of the first quarter.

I hope this helps, good luck! :D

5 0
2 years ago
Compare and contrast the average kinetic energy of 0.5 L of coffee at 34ÁC,
Andre45 [30]
Compared to coffee at room temperature, the molecules of the coffee at 34°C will be moving faster and colliding with one another more frequently.
6 0
3 years ago
A speed-time graph is shown below:
Juliette [100K]

Answer:

It traveled 4 centimeters.

Explanation:

In a speed versus time graph, the distance travelled is given by the area under the graph.

In this graph we have the following:

- The speed of the object is v = 1 cm/s between time t = 0 s and t = 4 s

- The speed of the object is v = 0 cm/s between time t = 4 s and t = 8 s

Since the speed in the second part is zero, the distance travelled in the second part is zero. So, the only distance travelled by the object is the distance travelled during the first part, which is equal to the area of the first rectangle:

d=v\Delta t=(1)(4-0)=4 cm

4 0
3 years ago
Raindrops fall vertically at 7.5 m/s relative to the Earth. What does an observer in a car moving at 20.2 m/s in a straight line
Vilka [71]

Answer:

vDP = 21.7454 m/s

θ = 200.3693°

Explanation:

Given

vDE = 7.5 m/s

vPE = 20.2 m/s

Required:  vDP

Assume that

vDE to be in direction of - j

vPE to be in direction of i

According to relative motion concept the velocity vDP is given by

vDP = vDE - vPE     (I)

Substitute in (I) to get that

vDP = - 7.5 j - 20.2 i

The magnitude of vDP is given by

vDP = √((- 7.5)²+(- 20.2)²) m/s =  21.7454 m/s

θ = Arctan (- 7.5/- 20.2) = 20.3693°

θ is in 3rd quadrant so add 180°

θ = 20.3693° + 180° = 200.3693°

4 0
3 years ago
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katovenus [111]

Explanation:

Though the diagram that is mentioned in the questions is not given. I have given general information related to the Earth's magnetic axis with respect to geographic/rotational axis.

Axis is an imaginary line around which a body rotates. The rotational axis of the Earth enters into and exits from the Earth at two points namely: North and South pole.

We know that the Earth behaves like a huge bar magnet so just like the bar magnet it must also have magnetic axis and poles. Earth has north magnetic pole and south magnetic pole. It has a strong magnetic field as well known as magnetosphere.

The interesting point about magnetic axis is that it is not same as rotational axis. In fact it makes an angle with the rotational axis. This is known as magnetic inclination. This inclination varies at different points on Earth.

Another interesting point is that the geographic and magnetic poles are opposite. That means near the geographic north pole we have the magnetic south pole and vice versa.

7 0
3 years ago
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