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Mrrafil [7]
3 years ago
6

Consider a car engine running at constantspeed. That is, the crankshaft of the en-gine rotates at constant angular velocity whil

eeach piston moves back-and-forth in its cylin-der according to the rules of simple harmonicmotion.2030 rpm6.95 cmSuppose the two extremal positionsxmaxandxminof a piston are 6.95 cm from eachother.When the crankshaft of the engine rotatesat 2030 rpm (revolutions per minute), what isthe maximal speed|v|maxof the piston?Answer in units of m/s.
Physics
1 answer:
Irina-Kira [14]3 years ago
7 0

Answer:

The value is  |v| = 7.39 \  m/s

Explanation:

From the question we are told that

    The angular speed is  w = 2030 \ rpm = \frac{2030 * 2 * \pi }{ 60} =  212.61 \ rad/s

    The distance between the minimum and maximum external position is  d = 6.95 \ cm  = 0.0695 \ m

Generally the amplitude of the crank shaft is mathematically represented as

         A =  \frac{d}{2}      

=>     A =  \frac{0.0695}{2}    

=>     A =  0.03475 \  m

Generally the maximum speed of the piston is mathematically represented as

        |v| = A * w  

=>    |v| = 0.03475 * 212.61

=>    |v| = 7.39 \  m/s

     

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(b). The direction of the first ball after the collision is 44.16° due south of east.

Explanation:

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Velocity of second ball u₂=- 0.80i m/s

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m = m_{1}=m_{2}

(a). We need to calculate the speed of the first ball after the collision

Using law of conservation of momentum

m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}

Along X- axis

m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}

v_{1}=u_{1}+u_{2}

Put the value into the formula

v_{1}=2.2i-0.80i

v_{1}=1.4i\ m/s

Along Y-axis

0=m_{1}v_{1}+m_{2}v_{2}

m_{1}v_{1}=-m_{2}v_{2}

v_{1}=-v_{2}

Put the value into the formula

v_{1}=-1.36j\ m/s

Then the final speed of the first ball

v_{1}=\sqrt{(1.4)^2+(1.36)^2}

v_{1}=1.95\ m/s

(b) We need to calculate the direction of the first ball after the collision

Using formula of direction

\tan\theta=\dfrac{v_{2}}{v_{1}}

\tan\theta=\dfrac{-1.36}{1.4}

\theta=\tan^{-1}\dfrac{-1.36}{1.4}

\theta=-44.16^{\circ}

Negative sign shows the direction of first ball .

Hence, (a). The speed of the first ball after the collision is 1.95 m/s.

(b). The direction of the first ball after the collision is 44.16° due south of east.

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