91Ó°ÊÓ

In physics, momentum is a fundamental concept that describes the motion of an object. It's a vector quantity, meaning it has both magnitude and direction, given by the product of an object's mass and velocity. For our raindrop, the mass is initially in grams and must be converted to kilograms for standard calculations. Hence, a raindrop with a mass of 0.014 g becomes 0.000014 kg when converted.
The formula for momentum (\(p\)) is:

• \[p = mv\]
• where \(m\) is the mass, and \(v\) is the velocity.

So, with a velocity of 8.1 m/s, the initial momentum is \(0.000014 kg \times 8.1 m/s\) which equals \(0.0001134 \text{ kg.m/s}\).
This tells us how much motion the raindrop carries before it hits the roof.

Impulse is a valuable concept in understanding how momentum changes when a force is applied. Impulse itself is a vector quantity and defined as the change in momentum. Here, as the raindrop makes contact with the roof and comes to rest, its final momentum becomes zero. Therefore, impulse \(J\) is calculated by subtracting the initial momentum \(p_{initial}\) from the final momentum \(p_{final}\).

• \[J = p_{final} - p_{initial}\]

In our problem, since \(p_{final} = 0\) (as the raindrop stops), and \(p_{initial} = 0.0001134 \text{ kg.m/s}\), the impulse is \(-0.0001134 \text{ kg.m/s}\).
The negative sign signifies the direction of the impulse, which matches the motion direction of the raindrop before impact.
The impulse is essentially how the raindrop's momentum stops and transfers to the roof upon impact.

Understanding force calculation helps us measure the effects of an impulse over a specific time. The average force during impact is derived from the impulse divided by the time interval during which the force acts. The equation is straightforward:

• \[F_{avg} = \frac{J}{t}\]

In the given problem, the impulse \(J\) is \(-0.0001134 \text{ kg.m/s}\), and the time \(t\) is 0.37 ms, which should be converted to seconds (0.00037 s) for accuracy.
When calculated, \(F_{avg} = \frac{-0.0001134}{0.00037}\) gives us an average force of \(-306.486 N\).
The negative sign indicates again that the force is exerted in the same direction as the raindrop's motion. The magnitude of the force, \(306.486 N\), tells us the average strength of the impact on the roof during the brief time span.