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igor_vitrenko [27]
3 years ago
15

To analyze the motion of a body that is traveling along a curved path, to determine the body's acceleration, velocity, and posit

ion.
A motorcyclist travels around a curved path that has a radius of 350 ft . While traveling around the curved path, the motorcyclist increases speed by 1.10 ft/s2

Part A - Finding the time interval for the motorcyclist to reach a given acceleration

If the motorcyclist starts from rest, determine the time needed to reach an acceleration of 5.25ft/s2

Part B - Speed of the Motorcyclist at a Given Acceleration

Determine the speed of the motorcyclist at the instant the acceleration is 6.75 ft/s2.

Part C - Magnitude of the Motorcyclist’s Acceleration at a Given Speed

Determine the magnitude of the acceleration at the instant the speed of the motorcyclist is 21.5 ft/s.

Part D - Maximum Constant Speed of the Motorcyclist

Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 6.75 ft/s2.
Physics
1 answer:
DiKsa [7]3 years ago
3 0

To solve this problem we will apply the kinematic equations of linear motion and centripetal motion. For this purpose we will be guided by the definitions of centripetal acceleration to relate it to the tangential velocity. With these equations we will also relate the linear velocity for which we will find the points determined by the statement. Our values are given as

R = 350ft

a_t = 1.1ft/s^2

PART A )

a_c = \frac{V^2}{R}

a_c = \frac{V^2}{350}

Calculate the velocity of the motorcycle when the net acceleration of the motorcycle is 5.25ft/s^2

a = \sqrt{a_t^2+a_r^2}

5.25 = \sqrt{(1.1)^2+(\frac{v^2}{350})^2}

27.5625 = 1.21 + \frac{v^4}{122500}

v=42.3877ft/s

Now calculate the angular velocity of the motorcycle

v = r\omega

42.3877 = 350\omega

\omega = 0.1211rad/s

Calculate the angular acceleration of the motorcycle

a_t = r\alpha

1.1 = 350\alpha

\alpha = 3.1428*10^{-3}rad/s^2

Calculate the time needed by the motorcycle to reach an acceleration of

5.25ft/s^2

\omega = \alpha t

0.1211 = 3.1428*10^{-3}t

t = 38.53s

PART B) Calculate the velocity of the motorcycle when the net acceleration of the motorcycle is 6.75ft/s^2

a = \sqrt{a_t^2+a_r^2}

6.75 = \sqrt{(1.1)^2+(\frac{v^2}{350})^2}

45.5625 = 1.21 + \frac{v^4}{122500}

v=48.2796ft/s

PART C)

Calculate the radial acceleration of the motorcycle when the velocity of the motorcycle is 21.5ft/s

a_r = \frac{v^2}{R}

a_r = \frac{21.5^2}{350}

a_r =1.3207ft/s^2

Calculate the net acceleration of the motorcycle when the velocity of the motorcycle is 21.5ft/s

a = \sqrt{a_t^2+a_r^2}

a = \sqrt{(1.1)^2+(1.3207)^2}

a = 1.7187ft/s^2

PART D) Calculate the maximum constant speed of the motorcycle when the maximum acceleration of the motorcycle is 6.75ft/s^2

a = \sqrt{a_t^2+a_r^2}

6.75 = \sqrt{(1.1)^2+(\frac{v^2}{350})^2}

45.5625 = 1.21 + \frac{v^4}{122500}

v=48.2796ft/s

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R= \frac{\omega _A}{\omega _B} 

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This can be rewritten as a function of the number of teeth of the gears. In fact, the angular velocity of a gear is inversely proportional to the radius r of the gear:
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3 years ago
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A simple machine consisting of an axle to which a wheel is fastened so that torque applied to the wheel winds a rope or chain onto the axle, yielding a mechanical advantage equal to the ratio of the diameter of the wheel to that of the axle.

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3 years ago
16x^2y^2-25a^2b^2<br>factorize the expression​
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Answer:

(4xy+5ab)(4xy-5ab)

Explanation:

16x^{2}y^{2}-25a^{2}b^{2}

4^2 is 16 and 5^2 is 25,

Also, (x-a)(x+a) = x^2-a^2

So, this factorized is:

(4xy+5ab)(4xy-5ab)

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8 0
3 years ago
a tank circuit contains a capacitor and an inductor that produce 30 of reactance at the resonant frequency. the inductor has a q
Romashka-Z-Leto [24]

The total circuit current at the resonant frequency is 0.61 amps

What is a LC Circuit?

  • A capacitor and an inductor, denoted by the letters "C" and "L," respectively, make up an LC circuit, also referred to as a tank circuit, a tuned circuit, or a resonant circuit.
  • These circuits are used to create signals at particular frequencies or to receive signals from more complicated signals at particular frequencies.

Q =15 = (wL)/R

wL = 30 ohms = Xl

R = 2 ohms

Zs = R + jXl = 2 +j30 ohms where Zs is the series LR impedance

| Zs | = 30.07 <86.2° ohms

Xc = 1/(wC) = 30 ohms

The impedance of the LC circuit is found from:

Zp = (Zs)(-jXc)/( Zs -jXc)

Zp = (2+j30)(-j30)/(2 + j30-j30) = (900 -j60)2 = 450 -j30 = 451 < -3.81°

I capacitor = 277/-j30 = j9.23 amps

I Zs = 277/(2 +j30) = (554 - j8,310)/904 = 0.61 - j9.19 amps

I net = I cap + I Zs = 0.61 + j0.04 amps = 0.61 < 3.75° amps

Hence, the total circuit current at the resonant frequency is 0.61 amps

To learn more about LC Circuit from the given link

brainly.com/question/29383434

#SPJ4

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1 year ago
Winds tend to rotate in a counter clockwise direction in the ___ (northern or southern) Hemisphere as they move into a low press
lana [24]

Answer:

Winds tend to rotate in a counter clockwise direction in the center of northern and southern hemisphere.

Explanation:

The wind blows clockwise around a high pressure area  in the northern hemisphere and the wind blows counter - clockwise around low pressure.  

In the northern hemisphere High-pressure systems rotate clockwise direction and in the southern hemisphere  low-pressure systems rotate clockwise direction.

 

8 0
3 years ago
Read 2 more answers
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