Average Force Question Given Velocities [High School]

[Liam C]

Homework Statement

Nikhil is probably eating his daily snack at this time. Old Man Miller comes back from the store and takes the 0.150kg sandwich from Nikhil as he begins to run away. Nikhil is running at 7.5m/s away from me when I hit him in the head with the sandwich that was moving at 17.5m/s when it makes contact with the back of his head. Determine the average force the sandwich applies to Nikhil's head if it is in contact with his head for a period of time which allows the sandwich to move 15cm forward before it falls to the ground.

Homework Equations

Where t is time:
t = Δd / (v1 + v2 / 2)
Where Vav is the average velocity:
Vav = Δd / Δt
Where Fav is the average force:
Fav = m × Vav / t

The Attempt at a Solution

m = 0.150kg
Δd = 15 cm = 0.15m
v1 = 17.5m/s
v2 = 0m/s
t = ?
Fav = ?

t = 0.15 / (17.5 / 2)
t = 0.017s

Vav = 0.15 / 0.017
Vav = 8.82m/s

Fav = (0.150)(8.82) / 0.017
Fav = 79N
∴ The average force applied to Nikhil's head by the sandwich is 79N

I was never taught average force in class so if my understanding is incorrect that is why. That is also why I am not confident in my answer and need help. Is my method correct, and if not where did I go wrong?

 

[scottdave]

There is debate about how to calculate average force. For the purpose of a high school problem, yours is about as good as another, I guess. One thing though: it looks like you have the sandwich going from 17.5 m/s down to zero m/s and take the 'average speed' of that. If the person continues to move forward at the same speed, then the sandwich will "fall off" the person when the sandwich starts to travel slightly slower than the person.

 

[Liam C]

There is debate about how to calculate average force. For the purpose of a high school problem, yours is about as good as another, I guess. One thing though: it looks like you have the sandwich going from 17.5 m/s down to zero m/s and take the 'average speed' of that. If the person continues to move forward at the same speed, then the sandwich will "fall off" the person when the sandwich starts to travel slightly slower than the person.

Oh! v2 is likely 7.5m/s then. Aha!

 

[haruspex]

There is debate about how to calculate average force.

Mmmm.. but perhaps in the same way that there is debate about evolution, climate change, vaccinations, ...
@LiamC, average force is defined as change in momentum divided by elapsed time. Unfortunately this question gives no way to find the elapsed time unless you assume the force is constant. If is constant then you can also calculate that force as work/distance, but also if it is constant there is no need to ask for the average.
So the question is fundamentally flawed, but perennially popular.

 

[Liam C]

Mmmm.. but perhaps in the same way that there is debate about evolution, climate change, vaccinations, ...
@LiamC, average force is defined as change in momentum divided by elapsed time. Unfortunately this question gives no way to find the elapsed time unless you assume the force is constant. If is constant then you can also calculate that force as work/distance, but also if it is constant there is no need to ask for the average.
So the question is fundamentally flawed, but perennially popular.

Wow that's very interesting, I'll have to bring that up with my teacher. I believe I'm learning "work" next week so I'm excited to find out what that means exactly.