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Elden [556K]
3 years ago
13

A force F with arrow= (5xî+ 4yĵ), where F with arrow is in newtons and x and y are in meters, acts on an object as the object mo

ves in the x direction from the origin to x = 5.01 m. Find the work W = F with arrow · dr with arrow done by the force on the object.
Physics
1 answer:
harkovskaia [24]3 years ago
6 0

Answer:

w= 62.75 J

Explanation:

Given that

Force vector F= 5 x i + 4 y j

Space vector or displacement vector d= 5.01 i

We know that work (w)

w=∫ F.ds

w= ∫(5 x i + 4 y j) .dx            ( only object is moving in x- direction)

w=\int_{0}^{5.01}5xi.dxi

w=\int_{0}^{5.01}5x.dx

w=\left [\dfrac{5}{2}x^2\right ]_0^{5.01}

w= 2.5 x 5.01² J

w= 62.75 J

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Answer:

The equation that will express this result os

h = 0 = vy t - 1/2 g t^2    so the net height traveled by the bullet is zero

vy t = 1/2 g t^2

vy = 1/2 g t

vy = 1/2 * 9.8 * t       you could use -9.8 to indicate vy and g are in different directions

tx = sx/ vx  = 46.4 / 471 = .0985 sec    time to travel up and down to original height

th = .0985 / 2 = .0493 sec        time to reach maximum height

vy = g ty = 9.8 * .0493 sec = .483 m/s    initial vertical speed

Sy = vy t - 1/2 g t^2 = .483 * .0493 - 1.2 9.8 (.0493^^2)

Sy = .0238 - 4.9 ( .0493)^2 = .0238 - .0119 = .0119 m

Height to which bullet will rise - if the gun is aimed at this height then in .0985 seconds the bullet will fall to zero height

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7 0
3 years ago
How many hours would it take for a single prokaryote, dividing every 20 minutes by binary fission in a favorable environment, to
butalik [34]

Answer:

170\frac{2}{3} hrs

Explanation:

in every 20 minutes the prokaryote divides to produce one of itself .

Mathematically,

20 mins:1 of its kind

x mins :512 of its kind

Where x is the amount of time (in minutes) needed by the prokaryote to produce 512 of its kind.

This implies that,

By cross multiplying we obtain,

x = 20 \times 512 = 10240mins

We now convert the time in minutes into hours.

Knowing very well that 60 minutes equals an hour, to convert 10240 minutes to hour we divide by 60.

This implies that,

10240 \div 60 = 170 \frac{2}{3}

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3 years ago
A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m. (i) What is the speed of waves on the s
bija089 [108]

Answer:

i

  v  = 142.595 \ m/s

ii

  f  = 109.69 \ Hz

iii1 )

  f_2 =219.4 Hz

iii2)

   f_3 =329.1 Hz

iii3)

    f_4 =438.8 Hz

Explanation:

From the question we are told that

    The length of the string is  l  = 0.65 \ m

     The tension on the string is  T  =  61 \ N

     The mass per unit length is  m =  3.0 \ g/m =  3.0 *  \frac{1}{1000} =  3 *10^{-3 } \ kg /m

     

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       v  = \sqrt{\frac{T}{m} }

substituting values

      v  = \sqrt{\frac{61}{3*10^{-3}} }

     v  = 142.595 \ m/s

generally the  string's  frequency is mathematically represented as

         f  = \frac{nv}{2l}

n = 1  given that the frequency we are to find is the fundamental frequency

So

      substituting values

       f  = \frac{142.595 * 1 }{2 * 0.65}

       f  = 109.69 \ Hz

The  frequencies at which the string would vibrate include

1       f_2 = 2 * f

Here f_2 is  know as the second harmonic and the value is  

      f_2 = 2 * 109.69

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2

f_3 =  3 * f

Here f_3 is  know as the third harmonic and the value is  

      f_3 = 3 * 109.69

     f_3 =329.1 Hz

3

     f_3 =  4 * f

Here f_4 is  know as the fourth harmonic and the value is  

      f_3 = 4 * 109.69

     f_4 =438.8 Hz

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