Question

To his surprise, Daniel found that an egg did not break when he accidentally dropped it from a height of 0.35 m onto his floor, covered with 3.0-cm-thick carpet.

Estimate the minimum acceleration of the egg while it was slowing down after touching the carpet.

Answer 1

The minimum acceleration of the egg while slowing down can be estimated using physics principles of deceleration. The formula a = Δv / Δt is applied, considering the change in velocity and time during the egg's impact with the carpet.

Step-by-step explanation:

Estimating the Minimum Acceleration of an Egg

To estimate the minimum acceleration of the egg while it was slowing down after touching the carpet, we need to apply the concepts of physics related to deceleration on impact. The carpet acts as a cushion, extending the time taken for the egg to come to a complete stop, thereby reducing the force exerted on it.

While we don’t have the exact time it took for the egg to stop, we can use the average acceleration formula a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time. Assuming the egg fell from rest and reached a velocity v just before impact (which can be found using v^2 = u^2 + 2as, where u is the initial velocity, a is the acceleration due to gravity, and s is the distance fallen), and it decelerated to a stop during its compression of the carpet.

The acceleration due to gravity is 9.81 m/s² and the distance s is 0.35 m. If we assume the egg comes to a stop in the 3.0 cm thickness of the carpet, we can estimate Δt based on the depth of the carpet and the velocity of the egg just before the impact, using the deceleration formula a = v^2 / (2s), where s is now the stopping distance, which is the thickness of the carpet.

Answer 2

`-112.7 m/s^2`

Step-by-step explanation:

We start by calculating the speed of the egg when it touches the upper surface of the carpet. This can be done by using the law of conservation of energy: in fact, the initial gravitational potential energy of the egg is converted into kinetic energy at the moment of impact, so we can write

`U=K\\mgh = (1)/(2)mv^2`

where

m is the mass of the egg

`g=9.8 m/s^2` is the acceleration of gravity

h = 0.35 m is the initial height of the egg

v is the speed as it touches the carpet

Solving for v,

`v=√(2gh)=√(2(9.8)(0.35))=2.6 m/s`

Now we analyze the motion of the egg through the carpet. The minimum acceleration will be obtained when the egg cover the whole tickness of the carpet to stop, that is

s = 3.0 cm = 0.03 m

And the egg must stop after covering this distance, so the final velocity will be

v' = 0

To find the acceleration, we can use the suvat equation:

`v'^2-v^2=2as`

and solving for a,

`a=(v'^2-v^2)/(2s)=(0^2-2.6^2)/(2(0.03))=-112.7 m/s^2`