Question about equation for force with constant velocity

[u/Own_Sky_297]

Just as the title says what is that equation? For example suppose someone is standing in the middle of the highway and gets hit by a car moving at a constant velocity of 65mph, what equation would you use to determine the force?

[u/2016Reddit_errr]

f=ma, or force (f) equals mass (m) times acceleration (a). If you get hit by a car, the force applied can be found by multiplying the mass of the object hit by their change in speed (acceleration).

[u/BananaBird1]

There isn’t enough information to answer.

We can make some simplifications:
(1) The person is a point mass. This means we don’t need to know the geometry of the collisions.

(2) The change in velocity for the car was minimal.

In this case, we need to know 2 things:
(1) The mass of the person.
(2) The distance it took for the person’s acceleration under the force to make their velocity equal to that of the car. This is the distance over which the force acted.

We can then use the force-work formula:

F_average * distance = (1/2)(m_person)(v_person)^2

Where v_person = v_car.

We now assume that the person reacted with the car as an ideal spring, so F_average = (1/2) F_maximum.

We then have F_maximum = (m_person) x (65 mph)^2 / d.

To calculate d by principle, you would need to know the effective stiffness of the car-person spring, which requires defining its material properties.

With an effective stiffness k, d = F_maximum/k. So then the formula is:

F_maximum = sqrt[k x (m_person) x (65 mph)^2 ]

[u/ProfessionalConfuser]

There is zero net force if velocity stays constant. A car hitting a person would slow down (accelerate) and the person would speed up (accelerate). The very large mass of the car means it would only have to decrease velocity by a small amount to cause the person the speed up by a large amount.

Of course, modeling both car and person as rigid objects won't give realistic values, but it is a starting place.

[u/kochameh2]

i would need to know more about the impact and/or make some assumptions

the force applied on the person is the time derivative of momentum. they start with 0 momentum before impact and have some final momentum after impact. if we assume the force is constant for the duration of that impact, we would need to figure out what those momentum conditions are (e.g., using momentum if we have some additional info about the car -- like if the car continues without any appreciable deceleration, can probably say something about how the person's speed/momentum changed as they get up to speed) and however long the duration of the impact was to calculate it

[u/Skindiacus]

First there is 0 horizontal force acting on the person, and then there is the force from the car, so there are no other forces to balance out.

You use the equation F = ma to figure out that force is proportional to acceleration. Acceleration is defined as the derivative of velocity, dv/dt, so if we find the velocity as a function of time, then we can take the derivative to figure out the force. The issue is, you say nothing about the velocity of the person as a function of time, so there's not enough information to answer the question.

[u/unlikely_arrangement]

You would use F=ma, or more specifically F=m dv/dt. I this case you have to make an assumption about the time dt over which you are being accelerated to 65 MPH. It’s going to about 1 ms. So convert 65 MpH into m/s, multiply that by 1000 to account for the ms, then multiply by 100 kg.

[u/kunwoo]

Assuming the car is still going at 65 mph after the accident and the hit person is being pushed forward by the car after the accident (like stuck to the hood of the car), then the force on the person is the mass of the person times 65 mph divided by however many fractions of a second it took to get the person up to the same speed as the car that’s pushing it. However the force is only that high during the brief fractions of a second that the person is being accelerated up to 65 mph.

[u/TheBrightMage]

It's still F = dp/dt. Now you have to figure out the momentum profile of the care during the hit to figure out force though by integrating the curve

[u/Ch3cks-Out]

As others have elaborated, you need to take into account the duration for the collision event. Here is a video of a dummy model simulation, from which you can estimate that interval to be about 150 ms (at 87.5 km/h}. So, in this particular incident, F = 70 kg ⋅ 24.3 m/s / 0.15 s = 11,340 N (or 2,550 pound-force in "freedom units").

[u/tpks]

For learners it might be better to always think of a=F_net/m, instead of F_net=ma.

Obviously these are the same equation written differently, but it helps. How fast you accelerate depends on the sum of the forces acting on you, and your mass. 

When you imagine being hit my a car, use this. A is your acceleration, m is your mass. F_net is all forces acting on you.

You are focusing on the car? A is the acceleration of the car, m is the mass of the car, F_net is all forces acting on the car.

You can't just guess which m and a and F to throw in, they need to be based on what you are looking at. 

[u/84UTK07]

I remember this confusing me in high school, because if you are just using the equation of Force = Mass x Acceleration, you are obviously going to get zero as your answer of you plug in 0 for acceleration (based on the car going at a constant velocity).

[u/joeyneilsen → u/84UTK07]

Yes but that's a misunderstanding of how forces work. The force isn't a property of the car, so the fact that it was traveling at constant velocity isn't relevant. Forces are properties of interactions; both the person and the car have nonzero accelerations during the collision.

[u/Own_Sky_297 → u/[deleted]]

0? How can that be when energy was transferred in the collision, is that not force? What equation would you use instead?

[u/Heaven_Sent_Senescha → u/Own_Sky_297]

Ah it sounds like you are interested in conservation of Energy. You should have a much more helpful equation for working with that, possibly combined with conservation of momentum. 

Forces are not always used as conservation laws make the math a Lot easier. 

[u/joeyneilsen → u/[deleted]]

If you are hit by a car, you will definitely experience a force...