You are trying to package a 50g egg so that it won't break after you drop it from a height of 10 meters. You decide to use wood as a nice soft packaging to protect the egg. When the egg hits the ground, the wood "softens" the landing so that it takes 5 milliseconds for the egg to come to rest. What is the average force on the egg when it lands?

Question

You are trying to package a 50g egg so that it won't break after you drop it from a height of 10 meters. You decide to use wood as a nice soft packaging to protect the egg. When the egg hits the ground, the wood "softens" the landing so that it takes 5 milliseconds for the egg to come to rest. What is the average force on the egg when it lands?

Answer 1

F delta t = change in momentum

F = .050 kg * v /5*10^-3 seconds
we need v
use conservation of energy
(1/2) m v^2 = m g h
v = sqrt (2gh) =sqrt (196) = 14 m/s
so
F = .05*14/5*10^-3 = 50*14/5 = 140 Newtons

Answer 2

To calculate the average force on the egg when it lands, we can use the equation for average force:

Average Force = Mass x Acceleration

First, let's calculate the mass of the egg. You mentioned that the egg weighs 50g, which is equivalent to 0.05 kilograms (since 1 kilogram = 1000 grams).

Now, let's calculate the acceleration. We can use the formula for acceleration:

Acceleration = Change in Velocity / Time

In this case, the change in velocity is the final velocity of the egg (which is 0 m/s since it comes to rest) minus the initial velocity. The initial velocity can be calculated using the formula for free-fall motion:

Initial Velocity = Square Root (2 x g x height)

Given that the height is 10 meters and g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth, we can compute the initial velocity.

After finding the initial velocity, we can calculate the acceleration using the formula above.

Once you have the mass and acceleration, you can multiply them together to find the average force on the egg.

So, to summarize the steps:

1. Convert the weight of the egg from grams to kilograms (50g = 0.05 kg).
2. Calculate the initial velocity of the egg using the formula Initial Velocity = Square Root (2 x g x height), where g is approximately 9.8 m/s^2 and height is 10 meters.
3. Calculate the acceleration using the formula Acceleration = Change in Velocity / Time, where the change in velocity is the final velocity (0 m/s) minus the initial velocity calculated in step 2.
4. Multiply the mass (0.05 kg) by the acceleration calculated in step 3 to find the average force on the egg when it lands.