This Ft = mv is very important, in fact, it can save your life. Seat belts, air bags, crumple zones and other car safety features are based on this formula.
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When you want to shrink the force of impact, you want to increase the time the impact takes. This is called the collision time. The longer the collision time the longer it takes your momentum to come to zero. Here’s the math.
If you are in a 1000 kg vehicle moving at 30 m/s your momentum is 1000 x 30 or 30,000 Ns ("Newton-seconds"). Now, lets say you hit a brick wall so your momentum goes from 30,000 to 0 in .5 seconds.
The equation we're going to use is the impulse-momentum change theorem: Ft = mv... so...
F x (0.5 seconds) = 30,000 Ns
so solve that equation for F= 60,000N!! That’s gonna leave a mark! Now lets say that instead of hitting a brick wall you hit a mound of hay and so the impact takes 3 seconds.
Now the formula looks like this: F x (3 seconds) = 30,000 Ns
and solve for force to get F= 10,000N.
Do you notice the difference? 60,000N versus 10,000N of force? All those safety features, seat belts, helmets, air bags, are designed to increase how long it takes your momentum to come to zero. Newton’s laws to the rescue! Let’s do a couple of experiments to help this information have more impact.
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[am4show have='p9;p58;' guest_error='Guest error message' user_error='User error message' ]
When you want to shrink the force of impact, you want to increase the time the impact takes. This is called the collision time. The longer the collision time the longer it takes your momentum to come to zero. Here’s the math.
If you are in a 1000 kg vehicle moving at 30 m/s your momentum is 1000 x 30 or 30,000 Ns ("Newton-seconds"). Now, lets say you hit a brick wall so your momentum goes from 30,000 to 0 in .5 seconds.
The equation we're going to use is the impulse-momentum change theorem: Ft = mv... so...
F x (0.5 seconds) = 30,000 Ns
so solve that equation for F= 60,000N!! That’s gonna leave a mark! Now lets say that instead of hitting a brick wall you hit a mound of hay and so the impact takes 3 seconds.
Now the formula looks like this: F x (3 seconds) = 30,000 Ns
and solve for force to get F= 10,000N.
Do you notice the difference? 60,000N versus 10,000N of force? All those safety features, seat belts, helmets, air bags, are designed to increase how long it takes your momentum to come to zero. Newton’s laws to the rescue! Let’s do a couple of experiments to help this information have more impact.
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Oops! You’re right! I have a calculator error on the video. I am so sorry about that! I should have checked the decimal places and seen that 300 million is not even in the ball park of the right answer, and should have been in the ten thousands. You have the correct answer at 83,540 lbf.
When we solve this, we get 83,540 lb. force. Can you help us? We converted mph to ft/s and got 80.7 ft/s. So then we multiplied weight 100 * 80.7, then divided by 32.2, then divided by .003.