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mixas84 [53]
2 years ago
11

For the ride to be comfortable, the magnitude of acceleration must not exceed 32 m/s2. What is the fastest constant speed that a

coaster can travel along this section of the track subject to this condition
Physics
1 answer:
VMariaS [17]2 years ago
7 0

Answer:

the maximum possible constant speed is  8 m/sec  

Explanation:

from the image, Given that

r(t) = (2t, t²,t²/3), -5 ≤ t ≤ 5  

Given that the curvature K(t)  = 2 / ( t² + 2)²  

note that t² + 2 ≥ 2  

(t² + 2)² ≥ 4

1 / (t² + 2)² ≤ 1/4

2 / (t² + 2)² ≤ 1/2

Also note that k(0) = 1/2

The normal component of acceleration satisfies aN = kv²

where v = ║v(t)║is the speed of the roller coaster.

The maximum possible normal component of acceleration is 32

so, aN ≤ 32 every where on the track

aN = kv² ≤  1/2v² ≤ 32

v² ≤ 64

Therefore, the maximum possible constant speed is  8 m/sec  

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A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 12 A, while that
andreev551 [17]

Answer:

a) 1450watts

b) 564watts

c) 1.11

Explanation:

Power consumed = IV

I is the current rating

V is the operating voltage

If a blow-dryer and a vacuum cleaner each operate with a voltage of 120 V and the current rating of the blow-dryer is 12 A, while that of the vacuum cleaner is 4.7 A then their individual power rating is calculated thus;

a) For blow-dryer

Operating voltage = 120V

Its current rating = 12A

Power consumed = IV

= 120×12

= 1440watts

b) For vacuum cleaner:

Operating voltage is the same as that of blow dryer = 120V

Its current rating = 4.7A

Power consumed = IV

= 120×4.7

= 564watts

c) Energy used = Power consumed × time taken

Energy used = Power × time

Energy used by blow dryer = 1440×20×60

= 1,728,000Joules

Energy used up by vacuum cleaner = 564×46×60

= 564×2760

= 1,556,640Joules

Ratio of the energy used by the blow-dryer in 20 minutes to the energy used by the vacuum cleaner in 46 minutes will be 1,728,000/1,556,640 = 1.11

4 0
3 years ago
What is the voltage of the electrochemical cell written as: Cu(s) | Cu2+(aq) || Mg2+(aq) | Mg(s)?
erma4kov [3.2K]
Thank you for posting your question here at brainly. Feel free to ask more questions.  
<span><span>The best and most correct answer among the choices provided by the question is  </span>B.-2.71 V.</span>  
Mg2+(aq) + 2e- -> Mg(s) E=-2.37 V  

Cu2+(aq) + 2e- -> Cu(s) E =+ 0.34 V  

Since Cu is acting as the anode, the equation needs to be reversed.  

Cu(s) -> Cu2+(aq) + 2e- E =- 0.34 V  

Ecell= -2.37 V+ (- 0.34 V) = -2.71 V   <span><span>

</span><span>Hope my answer would be a great help for you. </span> </span> <span> </span>
4 0
3 years ago
What is the available energy content, in joules, of a battery that operates a 2.00-W electric clock for 18 months
iren2701 [21]

Answer:

93312000 Joules

Explanation:

Energy can be explained as the capacity for doing work. And can be expressed as

E= pt....................eqn(1)

Where

E= Energy in Joules

P= power in Watt= 2.00W

t= time in seconds

Time= 18 months, which can be converted to "seconds" as;

18 months = [ 18 monthsx 30 days x 24 hours x 60 min x 60 sec] = 46656000

Then

time= 46656000 seconds

Power=2 watt

If we substitute into equation (1) we have

Energy = 2 watt × 46656000 seconds

Energy= 93312000 Joules

7 0
2 years ago
Ultraviolet (UV) radiation can be subdivided into three regions: UVA, UVB, and UVC, based on their energy. What are the minimum
ruslelena [56]

Answer:

100nm-280nm

Explanation:

Ultraviolet rays (UV) are part of the electromagnetic spectrum. It goes from 10nm to 400nm wavelengths, they are shorter than visible light, thus it's impossible to see by a human eye, and larger than X-rays (used in many medical applications and harmful when long-exposed).

According to its wavelengths, UV can be divided in different types:

UVA: long wave UV (315nm-400nm)

UVB: medium-wave UV (280nm-315nm)

UVC: short wave UV (100nm-280nm)

Therefore, UVC comprises wavelengths between 10nm and 280nm.

4 0
3 years ago
The work-energy principle states that the work done by all the __________ forces acting on an object (or system of objects) caus
CaHeK987 [17]

The work-energy principle states that the work done by all the non-conservative forces acting on an object (or system of objects) causes a change in the total mechanical energy of the object or system.


What is the work-energy principle?
The work-energy principle states that the total work done on a system is equal to the change in kinetic energy of the system. It is given as:

W.D = ΔK.E

       = K.E₁ - K.E₂

where K.E₁ is the initial kinetic energy of the system

            K.E₂ is the final kinetic energy of the system



What is meant by non-conservative forces?

Non-conservative forces as the name suggests are not conserved i.e. these forces cause a loss of mechanical energy from the system. A prime example of non-conservative forces is friction.

The total mechanical energy of the system is the sum of the potential energy and kinetic energy that the system contains. This energy is conserved and follows the work-energy theorem.

Learn more about work and energy here:

<u>brainly.com/question/17290830</u>

#SPJ4

4 0
2 years ago
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