Final answer:
A glass is less likely to shatter on a carpet than on hardwood because the carpet increases the duration of impact, spreading out the force over a longer time and reducing the average force on the glass.
Step-by-step explanation:
When two identical glasses are dropped from the same height with the same velocity, one onto a hardwood floor and another onto a carpet, the likelihood of the glass shattering is different due to the different impact forces experienced. This scenario showcases the relationship between the average impact force, the time duration of the impact, and the surface properties of the floor material.
According to the principles of physics, when an object strikes a surface, the change in momentum (which is the product of mass and velocity) will be the same regardless of the surface, since both glasses start with the same velocity and have the same mass. However, the average force exerted on the object is inversely proportional to the time duration over which the momentum change occurs, as stated by the impulse-momentum theorem. This means that if the time taken to stop the glass is longer, the average force exerted on it will be less.
A carpeted or padded surface provides a cushioning effect, increasing the time duration over which the glass comes to a stop. This extended time results in a reduced impact force compared to a hard surface like hardwood. Conversely, hardwood allows very little deformation, causing the glass to stop abruptly and experience a greater average force. This concept is analogous to the effect of an airbag in a car: increasing the duration of an impact reduces the force and, therefore, the likelihood of injury or breakage.
If the glass experiences an average force above a certain threshold, as in this case 330 Newtons (N), it will break. The average force can be calculated using the impact time and the object's mass and velocity just before impact. When impacting a softer surface like a carpet, the stopping time increases, which decreases the average force. Hence, a glass hitting a carpet is less likely to shatter than a glass hitting hardwood because the carpet extends the impact duration, thereby reducing the average force.