Compared to falling on a stone floor, a glass may not break when it falls on a carpeted floor because the (A) a) stopping time is longer on the carpet. (B) b) stopping time is shorter on the carpet. (C) c) carpeted floor provides a smaller impulse. (D) d) carpet provides a smaller impulse and a longer time.

To determine why a glass may not break when it falls on a carpeted floor compared to a stone floor, we need to analyze the concepts of impulse and stopping time. 1. **Impulse** is defined as the change in momentum of an object when a force is applied over a period of time. It can be calculated using the formula: \[ \text{Impulse} = \text{Force} \times \text{Time} \] 2. When an object falls and hits a surface, it experiences a force that stops it. The longer the stopping time, the smaller the average force exerted on the object, which can reduce the likelihood of breaking. 3. **Stopping Time**: On a carpeted floor, the stopping time is longer because the carpet compresses and allows the glass to decelerate more gradually compared to a hard stone floor, which stops the glass abruptly. Now, let's evaluate the options: - **(A)** a) stopping time is longer on the carpet. **(True)** This is a correct statement. - **(B)** b) stopping time is shorter on the carpet. **(False)** This is incorrect; the stopping time is longer on the carpet. - **(C)** c) carpeted floor provides a smaller impulse. **(False)** The impulse is related to the change in momentum, and while the force may be smaller due to longer stopping time, the impulse itself is not necessarily smaller. - **(D)** d) carpet provides a smaller impulse and a longer time. **(Partially True)** While the stopping time is longer, the statement about impulse being smaller is misleading without context. The best answer is **(A)** a) stopping time is longer on the carpet. This longer stopping time results in a smaller average force acting on the glass, reducing the chance of it breaking.