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A steel flat panel 6" X 18" weighing 3.25 pounds pivoted and fell 4 feet (center of gravity) striking a person flat on the head. What was the force that struck the person? This was an actual situation that raised a lump on the person's head.

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In summary, this person has a very specific situation that they hope to get a concrete answer to including equations and a step-by-step solution in inch/pounds/seconds units. They state that if they can ignore air resistance, they can calculate the speed of the plate just before it hit the head and the impulse exerted. If you were to take air resistance into consideration, the problem would become much more complex.

- #1

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A steel flat panel 6" X 18" weighing 3.25 pounds pivoted and fell 4 feet (center of gravity) striking a person flat on the head. What was the force that struck the person? This was an actual situation that raised a lump on the person's head.

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- #2

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You cannot in general say what this (maximum or average) force will be without knowing a bit more. If we ignore friction from air you could model the impact itself as a more or less elastic collision transferring momentum and energy from the plate to the head. To do this you would need to know how elastic the collision is, either by measurements or by a more detailed model of the plate bending dynamics. The latter would also enable you to get a rough estimate of the collision time and forces involved if force really is what you want.

What conclusion are you hoping to make based on knowing this force? Could you reach this conclusion in other ways?

- #3

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Like filiplarsen has mentioned, you'll need more details for more accurate measurements...

but if you were to simplify the case,

by ignoring air resistance

you could calculate the speed of the plate just before it hit the head by the work-energy theorem.

it comes out to be approx 16 feet/second

and if you take the (plate+earth) as the system, you could calculate the impulse imparted to the plate by the mans head due to the collision. This impulse would be equal to the change in momentum of the plate.

momentum of the plate(just before hitting the man's head) = mass.velocity = 52 pound feet/second

momentum of plate(after hitting the man) = 0

{ assuming the plate comes to rest, the collision being completely inelastic }

so, impulse exerted = change in momentum = 52-0 = 52 pound feet/second

and by Newton's third law, since every action, has an equal and opposite reaction, the impulse acted on the plate, would be the same as the impulse on the mans head.

so impulse exerted on the mans head = 52 pound feet/second

and furthermore, if you can measure the time for which the head and the plate are in contact, you could calculate the force acting on the man's head by dividing the impulse by the contact time.

assuming, the plate was in contact with the man's head for 0.01 seconds,

then force acting on the man's head = impulse/contact time = 52/0.01 = 5200 pound feet/(second)^2

that's equivalent to a mass of about 162.5 pounds.

but this will vary from the real case, as all this is done assuming air resistance isn't present..

If you were to take that into consideration... Well, the problem would become much more complex.

And also, i randomly assumed the contact time to be 0.01 seconds

even a small difference in this can make quite a difference.

besides, loads of other factors will come into play, like the compression offered by the hair, angle of striking.. The actual elasticity of the collision etc etc..

(and I'm not familiar with the british system of units of force and momentum so i just stuck with the basics..)

and yes, sorry for the lack of proper equations, but i have no access to a pc as of now and am posting this from my cell phone..

Hope this helps.

Cheers.

but if you were to simplify the case,

by ignoring air resistance

you could calculate the speed of the plate just before it hit the head by the work-energy theorem.

it comes out to be approx 16 feet/second

and if you take the (plate+earth) as the system, you could calculate the impulse imparted to the plate by the mans head due to the collision. This impulse would be equal to the change in momentum of the plate.

momentum of the plate(just before hitting the man's head) = mass.velocity = 52 pound feet/second

momentum of plate(after hitting the man) = 0

{ assuming the plate comes to rest, the collision being completely inelastic }

so, impulse exerted = change in momentum = 52-0 = 52 pound feet/second

and by Newton's third law, since every action, has an equal and opposite reaction, the impulse acted on the plate, would be the same as the impulse on the mans head.

so impulse exerted on the mans head = 52 pound feet/second

and furthermore, if you can measure the time for which the head and the plate are in contact, you could calculate the force acting on the man's head by dividing the impulse by the contact time.

assuming, the plate was in contact with the man's head for 0.01 seconds,

then force acting on the man's head = impulse/contact time = 52/0.01 = 5200 pound feet/(second)^2

that's equivalent to a mass of about 162.5 pounds.

but this will vary from the real case, as all this is done assuming air resistance isn't present..

If you were to take that into consideration... Well, the problem would become much more complex.

And also, i randomly assumed the contact time to be 0.01 seconds

even a small difference in this can make quite a difference.

besides, loads of other factors will come into play, like the compression offered by the hair, angle of striking.. The actual elasticity of the collision etc etc..

(and I'm not familiar with the british system of units of force and momentum so i just stuck with the basics..)

and yes, sorry for the lack of proper equations, but i have no access to a pc as of now and am posting this from my cell phone..

Hope this helps.

Cheers.

Last edited:

- #4

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i also made an assumption that the plate is a point object with a mass of 3.25 pounds..

I guess that about covers it..

The "Force of 6" x 18" Steel Panel Weighing 3.25 Pounds Striking a Person refers to the amount of impact or pressure that a steel panel weighing 3.25 pounds exerts on a person when it strikes them. This force is measured in pounds (lbs) and is a combination of the panel's weight and the speed at which it is moving.

The force of the steel panel can be calculated using the formula F = m x a, where F is the force in pounds, m is the mass of the steel panel in pounds, and a is the acceleration in feet per second squared. In this case, the acceleration is caused by the panel's speed and the force of gravity (32 ft/s^2).

The force of the steel panel can be affected by several factors, including the weight of the panel, the speed at which it is moving, the angle at which it strikes the person, and the surface area of contact. Additionally, the physical characteristics of the person being struck, such as their weight and body composition, can also impact the force felt.

The force of the steel panel can be dangerous to a person, depending on the circumstances. If the panel is moving at a high speed and strikes a person with a large surface area, it can cause significant injury or even death. However, if the panel is moving at a slow speed or strikes a person with a small surface area, the force may not be as dangerous.

The force of the steel panel can be reduced by decreasing its weight, slowing down its speed, or reducing the surface area of contact. Additionally, using protective gear or proper positioning can also help reduce the impact force on a person. It is important to take safety precautions and properly handle heavy objects to minimize the risk of injury from impact forces.

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