In a 49-second interval, 595 hailstones strike a glass window …

Physics Questions

In a 49-second interval, 595 hailstones strike a glass window with an area of 0.954 m² at an angle of 25° to the surface. Each hailstone has a mass of 7 g and a speed of 4.5 m/s. Assuming elastic collisions, what is the average force exerted on the window?

Short Answer

The answer discusses the concepts of elastic collision and momentum change regarding hailstones hitting a window. It details how to calculate the change in momentum for one hailstone and then applies that to a total of 595 hailstones to determine the average force exerted during the collisions, resulting in an average force of 0.323 N.

Step-by-Step Solution

1. Understand the Basics of Elastic Collision

In an elastic collision, objects collide and then bounce back without losing kinetic energy. For a hailstone, this means it returns with the same velocity after hitting the window. This property is essential for calculating changes in momentum and force during the collision.

2. Calculate Change in Momentum

To determine the change in momentum (√e¬ip) for one hailstone, you can use the formula: √e¬ip = 2 √o mass √o velocity. Given that the hailstone is hitting at an angle of 25¬∞, we adjust our calculations accordingly:

  • Mass of one hailstone = 0.007 kg
  • Velocity of hailstone = 4.5 m/s
  • Incline adjustment: sin(25¬¨‚àû)
  • Final calculation for one hailstone yields: ‚àöe¬¨ip ‚Äöaa 0.0266 kgm/s

3. Compute Average Force from Multiple Hailstones

When considering multiple hailstones, you multiply the change in momentum (√e¬ip) for one hailstone by the total number of hailstones. For 595 hailstones, the total change in momentum is: √e¬iP = 595 √o 0.0266. Finally, to find the average force (F), you use the formula F = √e¬iP/Œit, where Œit is the time interval of the collisions:

  • Total change in momentum for 595 hailstones = 15.82 kgm/s
  • Average force computation results in: F = 0.323 N

Related Concepts

Elastic Collision

An elastic collision is a type of collision where objects collide and bounce back without losing kinetic energy.

Change In Momentum

Change in momentum (œip) refers to the difference in momentum of an object before and after a collision and is calculated using the formula œip = 2 √o mass √o velocity.

Average Force

The average force (f) during a collision can be determined by calculating the total change in momentum (œip) divided by the time interval (œit) over which the collisions occur.

Scroll to Top