Question

Meteorite On October 9, 1992, a 27-pound meteorite struck a car in Peekskill, NY, creating a dent about 22 cm deep.

If the initial speed of the meteorite was 480m/s , what was the average force exerted on the meteorite by the car?

Express your answer using two significant figures.

Answer 1

I used kinematic equation: \[v _{f}^{2}=v _{i}^{2}+2ax\] \[a=\frac{ v _{f}^{2}-v _{i}^{2} }{ 2x }\]
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\[a=\frac{ (0m/s)^{2}-(480m/s)^{2} }{ 2(0.22m) }\]
\[a=25344m/s^{2}\]
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Then use force equation:
\[F=ma\]
\[F=12.247kg(25344m/s)^{2}\]
\[F=310000N\]
The website says my answer is wrong.
Can anyone tell me what I did wrong.

Answer 2

We need to use our work equation here!

The kinematic equation you used is only applicable in a very specific scenario of constant acceleration, where acceleration does not change with time nor distance travelled.

Here, the acceleration of the object changes because the force exerted on the meteorite by the car changes! This may be hard to realize at your current level of physics, but bear with me here.

Metals behave very much like springs when we apply forces to them. If you've studied springs, you'd realize right away that the force exerted by the spring depends on the position of the spring from some equilibrium point. \[F = kx\] where k is some constant the defines the stiffness of the spring, and x is the deflection of the spring.

The car behaves very much like a spring. When the meteorite first impacts the car, the force exerted by the deflecting metal is minimal. As the dent grows deeper and deeper, this force increases.

From Newton's First Law, \[F = ma\] we see that this changing force causes a proportional change in acceleration. This invalidates the above kinematic EOM (Equation of motion).

Now, back to the problem at hand.

If we don't know how a force evolves (or changes) over time or displacement, we can use work. Work is a state function. This means that it doesn't matter what path we take to get from point A to point B, it just matters the distance between point A and point B. Professor Walter Lewin, a physics professor at MIT, gives a great lecture on work. I'd recommend watching the entire 50 minute lecture. I've linked below to the specific part of the lecture where he illustrates the idea of "state" perfectly with his briefcase. http://youtu.be/CgqBg44azYk?t=6m40s

We need to also understand how work and energy are related. The work-energy theorem states that the amount of work done on an object creates for a change in energy or \[\Delta W = \Delta E\]

Understanding this leads us to use work to solve this problem.

The metoerite has an initial kinetic energy. The work done by the car to stop the meteorite brings this kinetic energy to zero.

The initial kinetic energy of the meteorite is \[KE = {1 \over 2} mv^2 = {1 \over 2} 12.25 [kg] \cdot {480^2} [m^2/s^4]\]

The amount of work done by the car on the meteorite is done over a distance of 22 cm and is expressed as\[W = F \cdot d = \Delta KE\]\[F_{car} \cdot 0.22 [m] = {1 \over 2} 12.25 \cdot 480^2\].

We can now find the force.

Answer 3

Wow. That makes a lot of sense. I feel enlightened haha. Thank you. I'll watch the video when I have the time.