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laiz [17]
3 years ago
14

A student wearing a frictionless roller skates on a horizontal is pushed by a friend with a constant force of 55N. How far must

the student be pushed, starting from rest, so that her final kinetic energy is 362 J
Physics
1 answer:
umka21 [38]3 years ago
3 0

Answer:

6.58m

Explanation:

The kinetic energy = Workdone on the roller

Workdone = Force * distance

Given

KE = Workdone = 362J

Force = 55N

Required

Distance

Substitute into the formula;

Workdone = Force * distance

362 = 55d

d = 362/55

d = 6.58m

Hence the student must push at a distance of 6.58m

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At t=0, a train approaching a station begins decelerating from a speed of 80 mi/hr according to the acceleration function a(t)=−
vredina [299]

Answer:

a)  Δx = 49.23 mi , b)  Δx = 5.77 mi

Explanation:

As we have an acceleration function we must use the definition of kinematics

     a = dv / dt

     ∫dv = ∫ a dt

we integrate and evaluators

      v - vo = ∫ (-1280 (1 + 8t)⁻³ dt = -1280 ∫ (1+ 8t)⁻³ dt

We change variables

       1+ 8t = u

       8 dt = du

       v - v₀ = -1280 ∫ u⁻³ du / 8

       v -v₀ = -1280 / 8 (-u⁻²/2)

       v - v₀ = 80 (1+ 8t)⁻²

We evaluate between the initial t = 0 v₀ = 80 and the final instant t and v

      v- 80 = 80 [(1 + 8t)⁻² - 1]

      v = 80 (1+ 8t)⁻²

We repeat the process for defining speed is

     v = dx / dt

    dx = vdt

    x-x₀ = 80 ∫ (1-8t)⁻² dt

    x-x₀ = 80 ∫ u⁻² dt / 8

    x-x₀ = 80 (-1 / u)

    x-x₀ = -80 (1 / (1 + 8t))

We evaluate for t = 0 and x₀ and the upper point t and x

   x -x₀ = -80 [1 / (1 + 8t) - 1]

We already have the function of time displacement

a) let's calculate the position at the two points and be

t = 0 h

     x = x₀

t = 0.2 h

    x-x₀ = -80 [1 / (1 +8 02) -1]

    x-x₀ = 49.23

displacement is

  Δx = x (0.2) - x (0)

   Δx = 49.23 mi

b) in the interval t = 0.2 h at t = 0.4 h

t = 0.4h

     x- x₀ = -80 [1 / (1+ 8 0.4) -1]

     x-x₀ = 55 mi

    Δx = x (0.4) - x (0.2)

     Δx = 55 - 49.23

     Δx = 5.77 mi

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A commuter train passes a passenger platform at a constant speed of 39.6 m/s. The train horn is sounded at its characteristic fr
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Complete Question

A commuter train passes a passenger platform at a constant speed of 39.6 m/s. The train horn is sounded at its characteristic frequency of 350 Hz.

(a)

What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding

(b) What wavelength is detected by a person on the platform as the train approaches?

 

Answer:

a

  \Delta  f  =  81.93 \ Hz

b

  \lambda_1 =  0.867 \ m

Explanation:

From the question we are told that

      The speed of the train is  v_t  =  39.6 m/s

      The frequency of the train horn is  f_t =  350 \ Hz

Generally the speed of sound has a constant values of  v_s  =  343 m/s

  Now  according to dopplers equation when the train(source) approaches a person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as  

        f_1 =  f *   \frac{v_s}{v_s - v_t}

substituting values

        f_1 =  350 *  \frac{343 }{343-39.6}

       f_1 =  395.7 \ Hz

  Now  according to dopplers equation when the train(source) moves away from  the  person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as  

           f_2 =  f *   \frac{v_s}{v_s +v_t}

substituting values

        f_2 =  350 *   \frac{343}{343  + 39.6}

       f_2 =  313.77 \ Hz

The overall change in frequency is detected by a person on the platform as the train moves from approaching to receding is mathematically evaluated as

        \Delta  f  =  f_1 - f_2

        \Delta  f  =  395.7 - 313.77

        \Delta  f  =  81.93 \ Hz

Generally the wavelength detected by the person as the train approaches  is mathematically represented  as

          \lambda_1 =  \frac{v}{f_1 }

          \lambda_1 =  \frac{343}{395.7 }

         \lambda_1 =  0.867 \ m

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