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- Homework Statement
- Let's suppose the head of a young football player has a mass of 4kg and a speed of 10m/s. If he was to collide without a helmet he basically has 1mm(0.001m) of cushion and increases the time the head stops in 0.0005secs. If a helmet provides 20mm(0.02m) of cushion and increases the time the head comes to rest to 0.002 secs. Find the momentum change of his head for both collisions. Find the momentum change of his head for both collisions. Find the force on the head both with and without a helmet.

- Relevant Equations
- Impulse - momentum theorem

Without helmet, m = 4kg, ##v_f = 10m/s## ##\Delta t = 0.0005sec##

$$ \Delta p = mv_f - mv_i $$

$$ \Delta p_{without} = 40 kg m/s$$

$$ Impulse_ {without} = F_{net} \cdot \Delta t$$

$$ force_{without} = 80000 N$$

With helmet m = 4kg, ##v_f = 10m/s## ##\Delta t = 0.002sec

$$ \Delta p = mv_f - mv_i $$

$$ \Delta p_{with} = 40 kg m/s$$

$$ Impulse_ {with} = F_{net} \cdot \Delta t$$

$$ force_{with} = 20000N$$

I'm just confused with the velocity in the question above. Are they stating initial or final? In my derivation above, I took it as the final velocity.

And it looks like the answer to force without and with the helmet are wrong.

$$ \Delta p = mv_f - mv_i $$

$$ \Delta p_{without} = 40 kg m/s$$

$$ Impulse_ {without} = F_{net} \cdot \Delta t$$

$$ force_{without} = 80000 N$$

With helmet m = 4kg, ##v_f = 10m/s## ##\Delta t = 0.002sec

$$ \Delta p = mv_f - mv_i $$

$$ \Delta p_{with} = 40 kg m/s$$

$$ Impulse_ {with} = F_{net} \cdot \Delta t$$

$$ force_{with} = 20000N$$

I'm just confused with the velocity in the question above. Are they stating initial or final? In my derivation above, I took it as the final velocity.

And it looks like the answer to force without and with the helmet are wrong.

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