An egg in a special container together have a mass of 148.0 g. The container is designed such that when dropped it will bring the egg to a stop in 0.200 s when it hits the ground. A force of 4.91 N will break the egg. What is the maximum height from which the egg in its container can be dropped and not break the egg?
Question
An egg in a special container together have a mass of 148.0 g. The container is designed such that when dropped it will bring the egg to a stop in 0.200 s when it hits the ground. A force of 4.91 N will break the egg. What is the maximum height from which the egg in its container can be dropped and not break the egg?
Solution
To solve this problem, we need to use the principles of physics, specifically the concepts of force, mass, acceleration, and gravity. Here are the steps:
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First, we need to find the mass of the egg. We know that the mass of the egg and the container together is 148.0 g, but we need the mass in kilograms (since we're dealing with Newtons and meters/second^2, which are standard SI units). So, we convert 148.0 g to kg by dividing by 1000, which gives us 0.148 kg.
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Next, we need to find the maximum deceleration the egg can withstand without breaking. We know that force equals mass times acceleration (F = ma), so we can rearrange this equation to solve for acceleration (a = F/m). Plugging in the values we know (F = 4.91 N, m = 0.148 kg), we get a = 4.91 N / 0.148 kg = 33.18 m/s^2. This is the maximum deceleration the egg can withstand without breaking.
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Now, we need to find the maximum height from which the egg can be dropped. We know that the container will bring the egg to a stop in 0.200 s, so we can use the equation for motion under constant acceleration (d = vit + 0.5at^2) to find the distance (d). However, since the egg starts from rest, the initial velocity (vi) is 0, so the equation simplifies to d = 0.5at^2. Plugging in the values we know (a = 33.18 m/s^2, t = 0.200 s), we get d = 0.5 * 33.18 m/s^2 * (0.200 s)^2 = 0.664 m.
So, the maximum height from which the egg in its container can be dropped and not break the egg is 0.664 meters.
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