An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the momentum of each object by multiplying its mass and velocity.
Determine the momentum for object W: 12 × 5 = 60 .
Determine the momentum for object X: 15 × 8 = 120 .
Determine the momentum for object Y: 18 × 2 = 36 .
Determine the momentum for object Z: 28 × 10 = 280 .
List the objects in order of increasing momentum: Y , W , X , Z .
Explanation
Understanding the Problem We are given the masses and velocities of four objects and asked to list them in order of increasing momentum. Momentum is calculated as the product of mass and velocity.
Calculating Momentum First, we calculate the momentum of each object:
Object W: Momentum = Mass × Velocity = 12 k g × 5 m / s = 60 k g ⋅ m / s Object X: Momentum = Mass × Velocity = 15 k g × 8 m / s = 120 k g ⋅ m / s Object Y: Momentum = Mass × Velocity = 18 k g × 2 m / s = 36 k g ⋅ m / s Object Z: Momentum = Mass × Velocity = 28 k g × 10 m / s = 280 k g ⋅ m / s
Comparing Momentum Now, we compare the momentum of the four objects:
Object Y has the least momentum: 36 k g ⋅ m / s Object W has the next least momentum: 60 k g ⋅ m / s Object X has the next least momentum: 120 k g ⋅ m / s Object Z has the greatest momentum: 280 k g ⋅ m / s
Listing in Order Therefore, the objects in order from least to greatest momentum are Y, W, X, Z.
Examples
Understanding momentum is crucial in many real-world scenarios, such as car safety. When designing vehicles, engineers consider the momentum involved in collisions to develop effective safety measures like airbags and crumple zones. These features help to reduce the force experienced by passengers by increasing the time over which the momentum changes during an impact. This ensures that the change in momentum occurs over a longer period, reducing the force and minimizing injuries.
To find the number of electrons that flow through a device with a current of 15.0 A for 30 seconds, we first calculate the charge using Q = I × t , yielding 450 C. Then, using the charge of a single electron (approximately 1.6 × 1 0 − 19 C), we find that approximately 2.81 × 1 0 21 electrons flow through the device.
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