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 550 m/s, what was the average force exerted on the meteorite by the car?
To find the average force exerted on the meteorite by the car, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) multiplied by the acceleration (a).
However, we don't have the acceleration directly given, but we can calculate it using the equation of motion for constant acceleration: s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Here's how we can calculate the acceleration using the given information:
Given:
Initial velocity (u) = 550 m/s
Displacement (s) = -0.22 m (negative because the meteorite dented the car inward)
Since we are not given the time, we cannot calculate it directly. However, if we assume that the meteorite came to a stop upon impact, we can determine the time taken to stop using the equation v = u + at, where v is the final velocity (which we assume to be 0 m/s).
0 = 550 + a * t
a * t = -550 ...(1)
Now, solving the equation of motion for displacement:
-0.22 = (550 * t) + (0.5 * a * t^2) ...(2)
Using equation (1), we can substitute the value of a * t as -550:
-0.22 = 550t - 0.5 * 550 * t^2
-0.11 = 275t - 0.25t^2
0.25t^2 - 275t - 0.11 = 0
This is a quadratic equation that can be solved to find the value of t. Once we have t, we can substitute it into equation (1) to calculate the acceleration (a).
Once we have the acceleration, we can determine the average force exerted on the meteorite by the car using Newton's second law:
Force (F) = mass (m) * acceleration (a)
To convert the mass from pounds to kilograms, we use the conversion factor of 1 lb = 0.4536 kg.
Note: Due to the complexity of the calculations involved, it is recommended to use a scientific calculator or solve the equation using a mathematical software program or spreadsheet.