what is used to determine the force of impact from vehicle

If you have watched MythBusters, you are aware that they often crash things into each other. In the latest episode, the MythBusters dropped a piano onto the roof of a house. Before the drop, they stated that the piano weighed 700 pounds and would be dropped fifty feet above the roof. Right earlier impact, the piano would be traveling at 38 mph and accept an bear on force of 12,000 pounds.

So, how did they get these values? Clearly they could simply measure the mass and the starting height. But what about the speed and the impact forcefulness? Permit me show you how you calculate these values. The groovy thing about this pianoforte drop is that it'south a perfect introductory physics trouble that uses both the Piece of work-Energy Principle and the Momentum Principle.

Touch on Speed

This is the simplest function of the problem. How fast was the piano right before it hit the roof? Here is a diagram.

I'm going to use the work-energy principle to find the speed. Sure, you could use i of the kinematic equations but it isn't as clear as the piece of work-energy principle. The work-energy principle says that if y'all have some arrangement, the work done on it is the change in free energy of that organization. If I merely but use the piano equally the system then the but kind of energy it could take would exist kinetic energy. I can write this equally:

When calculating the work done by some strength, Δr is the distance over which that force is applied and θ is the angle betwixt the force and the displacement. But why is this a work-energy problem? Since work deals with changes in energy over distance it is best to employ work-free energy when you lot take something starting and catastrophe at ii different positions. At present, if the problem said the piano dropped for a time interval of 3 seconds it would be rather difficult to calculate this with the work-energy principle.

In society to employ the work energy, I need to find what forces do piece of work on the pianoforte as it falls. Actually, there is merely one force on the pianoforte - the gravitational force. But should there exist a gravitational potential energy? Yes, you could practise it that way if you chose the Piano and the Earth equally the system. In that case, there would be a gravitational potential free energy simply no piece of work done by gravity. You can't have it both ways. That would exist like having your cake and eating information technology too.

Since the gravitational strength is pulling in the aforementioned direction every bit the pianoforte is moving, θ would exist zippo. The piece of work done would then exist:

This work would be equal to the change in kinetic free energy. Since the pianoforte starts from balance, the initial kinetic free energy is zero. At present I tin put this together and solve for the final velocity.

Find that the mass cancels. Now put in a height of 15.24 meters and value for yard of 9.viii m/s² and you get a final speed of 17.28 m/s. Convert this to mph and you go 38.seven mph. That's substantially the answer they said on the bear witness. Oh, hither'southward tip - simply blazon into google: "17.28 grand/s in mph" and you will get the conversion.

But what about air resistance? I am going to guess that the air resistance as this piano falls is negligible. You tin find the final velocity if air resistance is included every bit a homework problem.

Of grade y'all could check this reply without as well much effort. If you lot did a video analysis of the falling pianoforte, you could get the velocity right before it hits. I'one thousand pretty sure y'all would get about fifteen m/s.

Affect Force

I'll be honest. This is a much harder problem. How difficult does something hit? There are just and then many things that factor into a collision that information technology makes it quite difficult to narrate. I've looked at this problem of standoff characterizing before. But in the terminate, everyone wants i number for the collision and "impact force" is usually what people end up with.

So as this piano collides with the roof, how could you estimate this bear on forcefulness? Permit'due south start with the momentum principle. This gives a relationship betwixt the net force on an object and that object'due south change in momentum.

I tin use this on the colliding pianoforte. I know the starting momentum (from the velocity right before it collides). I also know the concluding momentum since I tin assume information technology comes to a rest. I don't know the fourth dimension interval. The time interval is the key. Since we know the estimated impact force from the show (12,000 pounds = 53,379 Newtons), the impact fourth dimension can be calculated.

Let me commencement with a force diagram showing the forces acting on the piano during the collision.

There are 2 forces acting on the piano: gravity and the roof pushing up. The force the roof pushes up is the aforementioned strength that the piano pushes on the roof - this is the impact strength. Since this all happens just in the vertical direction, I can write this as the scalar equation:

Just to be clear: the final velocity is zip and the initial velocity is in the negative y-direction. That is why I accept 0 - (-mv_ane). Now, I know everything in this expression except for Δt. Putting in the values for the knowns, I go a time interval of 0.109 seconds. Permit'south just telephone call it 0.ane seconds.

Then, if you assume that the touch happens in 0.1 seconds and so the average affect force would exist 12,000 pounds. But is 0.one seconds a reasonable approximate for the collision fourth dimension? 1 manner to think of this would be to determine the distance the piano moves during this collision. I can do this with the definition of average velocity (in the y-management):

The piano starts at 17.28 chiliad/s and ends at 0 m/s. This means that the average velocity would be (17.28 m/southward)/2. Since I know the time interval, I tin calculate the modify in vertical position. This gives a collision distance of 0.86 meters.

Could the middle of the piano move 0.86 meters during the collision? I say yes. That means an impact force of 12,000 pounds is PLAUSIBLE.

Ok, what about another example? Later, the MythBusters dropped a two,600 pound piano (filled with sand) from a meridian of 75 anxiety. They estimated an touch force of 55,000 pounds. If I convert these values and do exactly the same thing equally before, what value do I get for impact time? Starting time, I get an impact velocity of 21.6 m/southward and 2nd I become a standoff time of 0.107 seconds (or 0.1 seconds).

What if you lot modify the collision time?

Just for fun, what if the collision time was a piddling longer or a little shorter? All I need to practise is to rearrange the momentum principle equation above to solve for the force the roof pushes on the piano instead of the fourth dimension. Now if I put in different impact times, I become the following plot.

A big increase in collision time can mean subtract in impact force. This is substantially what an air bag in your car does. It increases the fourth dimension over which it stops you and decreases the force.

But what if the piano didn't stop? What if the piano kept falling down as it crashed through the roof? In this instance, the pianoforte would accept a smaller change in momentum and a smaller impact forcefulness. What if the piano bounced back upward during the collision? Since momentum is a vector, a piano going down and so up would have a much larger change in momentum than one that just stops. This would increase the touch on forcefulness.

Another Estimation of Bear upon Force

It's difficult to gauge the touch on time. What if instead of getting an impact time interval, you estimated the bear upon distance? This is the distance that the pianoforte moves while colliding with the roof - allow's call this distance due south. In this case, you wouldn't utilize the momentum principle to find the touch force since you don't have a time. Instead, you would once again utilize the work-free energy principle. As the pianoforte collides with the roof, there are 2 forces that do work. In that location is the gravitational force and the roof force. If I assume the pianoforte stops, I could write the work-energy equation every bit:

With this method, y'all go almost the aforementioned impact force if you use a collision distance of 0.86 meters (with some rounding error). Hither is a more dramatic case of this same adding with the collision of Iron Human with the ground.

How Could Yous Measure the Bear upon Strength?

Maybe an estimate isn't skilful enough for you. Maybe you lot desire to measure the impact force. Here are some ideas that what sort of piece of work.

• Place an accelerometer on the piano. As the piano collides with the roof, information technology volition have an acceleration. By measuring the acceleration, you lot calculate the net strength on the piano and also the force the roof exerts on the piano.
• Use high speed video to get an accurate estimate of the collision time. Next use the above calculations to determine the forcefulness.
• Apply high speed video to get an authentic estimate of the impact distance. Over again, use the to a higher place calculations to find the force.
• They practice make force sensors. You could drib the piano on top of one of these sensors and it would tape the strength as a function of time. However, you lot wouldn't be dropping the piano straight onto the roof, would you?

If you want to decide beforehand if the roof volition break, you lot have a nearly impossible task. Only imagine if the piano commencement contacted the roof with just the corner of the pianoforte. I this case, at that place would exist an impact force on the roof. But since simply a modest area of the piano is in contact, the pressure level on the roof will be high. I doubtable that the biggest gene for breaking is maximum pressure.

How do yous estimate the pressure in a collision? That's just a tough job. I call back I take washed something like this before, but I tin't remember where. Update: I simply remembered my more detailed collision interpretation. Tin can Bird Poop Crack a Windshield?

Homepage image: Filter Commonage/Flickr

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Source: https://www.wired.com/2014/07/how-do-you-estimate-impact-force/

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