a large bedsheet is held verticallyy by two students. A third student who happens to be the star pitcher on the baseball team, throws a raw egg at the sheet. explain why the egg doesn't break when it hits the sheet, regardless of its initial speed.

Assume that the bed sheet is of light material and deflects a lot when the egg hits it in the middle.

Force = momentum change / time change = m delta v / delta t ---> m a
The force on the egg is the
mass of the egg * speed of egg when it hits / time to stop

the time to stop is the stopping distance /average speed during stop which is half the initial speed

so if stopping distance is d, initial speed is v and egg mass m then
F = m v / [ d/.5 v ] = .5 m v^2/d

(this is of course just the same as saying the work done by the sheet on the egg is the change in kinetic energy of the egg)

The bigger d, the stopping distance, the smaller the force F.

When the raw egg hits the sheet being held vertically by two students, it doesn't break due to a concept called the conservation of momentum. The conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting upon it.

In this scenario, when the egg hits the sheet, it exerts a force on the sheet while also experiencing an equal and opposite force from the sheet, according to Newton's third law of motion. These forces result in a change in momentum of both the egg and the sheet.

However, the sheet being held tightly by the two students acts as an external force on the egg, slowing down its momentum gradually. This reduces the force of impact on the egg, decreasing the chances of it breaking. The flexible and moving nature of the sheet absorbs and distributes the force of the egg's impact across its surface, preventing the egg from experiencing a high localized force that could break it.

Additionally, the large surface area of the sheet spread out the force over a larger area, further reducing the impact on any particular spot and thus minimizing the chance of the egg breaking.

Therefore, by utilizing the principles of the conservation of momentum, the external force provided by the sheet, and the distribution of force through a large surface area, the egg doesn't break when it hits the sheet, regardless of its initial speed.

When the raw egg hits the bedsheet held vertically by two students, it doesn't break, regardless of its initial speed, due to a concept called impulse and momentum.

Impulse is defined as the change in momentum of an object. Momentum, on the other hand, is the product of an object's mass and velocity. When the egg hits the bedsheet, the impulse acting on the egg depends on the time it takes for the egg to come to a stop.

Usually, when an egg hits a solid surface, it quickly comes to a stop. The sudden change in momentum results in a large force acting on the egg, causing it to break. However, in this scenario, the bedsheet allows the egg to come to a stop over a longer period of time. This increased time interval for the egg to stop reduces the force acting on it, preventing it from breaking.

The bedsheet acts as a cushion, distributing the force of the impact evenly over a larger surface area. The fabric of the bedsheet deforms, absorbs some of the egg's kinetic energy, and provides a longer stopping time. This gradual decrease in momentum decreases the force exerted on the egg, minimizing the chance of it breaking upon impact.

In summary, the raw egg doesn't break when it hits the bedsheet because the fabric allows for a longer stopping time, reduces the force exerted on the egg, and provides a cushioning effect to absorb the energy of the impact.