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Engineering
11 months, 1 week ago

Help me understand! If Force F= 500- 100t, then impulse as a function of time will be:

If Force F= 500- 100t, then impulse as a function of time will be: 

  • Option 1)

    500t - 50 t^{2}

  • Option 2)

    50t-10

  • Option 3)

    50 - t^{2}

  • Option 4)

    -\alpha v^{2}

 
Answers (1)
571 Views
P Plabita
Answered 11 months, 1 week ago

As discussed in

Impulse Momentum Theorem -

\vec{F}=\frac{d\vec{p}}{dt}

\int_{t_{1}}^{t_{2}}\vec{F}dt=\int_{p_{1}}^{p_{2}}\vec{dp}

- wherein

If \bigtriangleup t  is increased, average force is decreased

 

 f = 500-100d

 

dp = f\cdot dt = \int_{P_{i}}^{P_{t}}dP= \int (500-100d)dt

P_{t}-P_{i} = 500t - 100\frac{p^{2}}{2}

\Delta P=I (Change in linear Momentum = Impulse)

\therefore I=500t-500t^{2}

 


Option 1)

500t - 50 t^{2}

This solution is correct.

Option 2)

50t-10

This solution is incorrect.

Option 3)

50 - t^{2}

This solution is incorrect.

Option 4)

-\alpha v^{2}

This solution is incorrect.

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