How to work out this impact force

[Lily May]

Homework Statement

During a Formula 1 race a car that was traveling at a speed of 172.8 km/h crashed into a wall. When the car hit the wall it came to a complete stop in 0.0272 s. If the driver of the car holds a mass of 70kg, calculate the impact force he experienced.

Homework Equations

I honestly don't know. F = m*a or F= GMm/r^2

The Attempt at a Solution

I have no idea what to do?
F= m*a
= 70*172.8
= 12 096N

 

[DrClaude]

Homework Equations

I honestly don't know. F = m*a or F= GMm/r^2

I don't think gravity will have anything to do with this problem, so you can forget that last equation.

The Attempt at a Solution

I have no idea what to do?
F= m*a
= 70*172.8
= 12 096N

What is the acceleration (meaning "deceleration" in this case) of the car as it hits the wall?

 

[Drakkith]

F= m*a
= 70*172.8

Does the unit for acceleration match the unit of the number you've plugged in for 'a'? If not, how might you get that unit from the information provided?

 

[Lily May]

I don't think gravity will have anything to do with this problem, so you can forget that last equation.What is the acceleration (meaning "deceleration" in this case) of the car as it hits the wall?

Am I meant to use the acceleration formula for that?
a= v1 - v2 / t

 

[DrClaude]

Am I meant to use the acceleration formula for that?
a= v1 - v2 / t

Yes. [But it should be v2 - v1 if v2 is the final velocity. And parentheses can be helpful: a = (v2 - v1)/t.]

 

[Lily May]

Does the unit for acceleration match the unit of the number you've plugged in for 'a'? If not, how might you get that unit from the information provided?

So you'd have to mutiple the number by 1000 then divide by 3600?
172.8*1000= 172800
172800/3600= 48m/s/s

 

[DrClaude]

So you'd have to mutiple the number by 1000 then divide by 3600?
172.8*1000= 172800
172800/3600= 48m/s/s

Put units everywhere:
$$
\begin{align*}
172.8\frac{\mathrm{km}}{\mathrm{h}} \times \frac{1000\ \mathrm{m}}{\mathrm{km}} &= 172800 \frac{\mathrm{m}}{\mathrm{h}} \\
172800 \frac{\mathrm{m}}{\mathrm{h}} \times \frac{\mathrm{h}}{3600\ \mathrm{s}} &= 48 \frac{\mathrm{m}}{\mathrm{s}}
\end{align*}
$$

 

[Lily May]

Yes. [But it should be v2 - v1 if v2 is the final velocity. And parentheses can be helpful: a = (v2 - v1)/t.]

So
v2 = 0?
v1= 48m/s^2
t = 0.0272s

 

[Drakkith]

So you'd have to mutiple the number by 1000 then divide by 3600?
172.8*1000= 172800
172800/3600= 48m/s/s

DC seems to be helping you well at the moment. I'm going to step out and let him handle it for now. I'll pop back in later though.

 

[Lily May]

Put units everywhere:
$$
\begin{align*}
172.8\frac{\mathrm{km}}{\mathrm{h}} \times \frac{1000\ \mathrm{m}}{\mathrm{km}} &= 172800 \frac{\mathrm{m}}{\mathrm{h}} \\
172800 \frac{\mathrm{m}}{\mathrm{h}} \times \frac{\mathrm{h}}{3600\ \mathrm{s}} &= 48 \frac{\mathrm{m}}{\mathrm{s}}
\end{align*}
$$

Whoops, I'll be sure to do that, thanks. So then do I use the acceleration fomula or the force fomula?

 

[DrClaude]

So
v2 = 0?
v1= 48m/s^2
t = 0.0272s

Are you sure about the units of v1? What is the acceleration?

 

[Lily May]

Are you sure about the units of v1? What is the acceleration?

v1 = 48m/s
a = (v2 - v1)/t.]
= 0 - 48m/s
= -48m/s / 0.0272s
a = -1 764.71m/s
that doesn't seem right

 

[jbriggs444]

v1 = 48m/s
a = (v2 - v1)/t.]
= 0 - 48m/s
= -48m/s / 0.0272s
a = -1 764.71m/s
that doesn't seem right

Units... if you divide meters per second by seconds, what do you get?

 

[Drakkith]

v1 = 48m/s
a = (v2 - v1)/t.]
= 0 - 48m/s
= -48m/s / 0.0272s
a = -1 764.71m/s
that doesn't seem right

The math looks correct, you just have it in units of velocity instead of acceleration.

 

[Lily May]

The math looks correct, you just have it in units of velocity instead of acceleration.

So I'd just change the end to -1 764.71m/s^2 = a
And mass = 70kg
Then I multiple those two together to get the impact force/final answer?

 

[DrClaude]

So I'd just change the end to -1 764.71m/s^2 = a
And mass = 70kg
Then I multiple those two together to get the impact force/final answer?

Correct.

 

[Lily May]

Correct.

Thank you all!

 

[BvU]

Bit of a macabre exercise. 180 g can not be survived by a human. This looks like a post mortem review ..
Fortunately head-on crashes with concrete walls are rare in F1.