An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

Calculate the speed using the formula v = r \[ O m e g a ] : v = 2.5 m × 10 r a d / s = 25 m / s .
Calculate the centripetal acceleration using the formula a = r \[ O m e g a ] 2 : a = 2.5 m × ( 10 r a d / s ) 2 = 250 m / s 2 .
Compare the calculated speed and acceleration with the values in the table.
The correct row is row 1, so the answer is a ​ .

Explanation

Problem Analysis We are given a hammer thrower swinging a hammer in a horizontal circle with a radius of 2.5 m and an angular velocity of 10 rad/s. We need to find the speed and magnitude of the acceleration of the ball just before release.

Calculating the Speed First, we calculate the speed v of the ball using the formula v = r \[ O m e g a ] , where r is the radius and \[ O m e g a ] is the angular velocity. In this case, r = 2.5 m and \[ O m e g a ] = 10 r a d / s . Therefore, v = 2.5 m × 10 r a d / s = 25 m / s .

Calculating the Acceleration Next, we calculate the centripetal acceleration a of the ball using the formula a = r \[ O m e g a ] 2 . Substituting the given values, we have a = 2.5 m × ( 10 r a d / s ) 2 = 2.5 m × 100 ( r a d / s ) 2 = 250 m / s 2 .

Finding the Correct Row Comparing our calculated values with the table, we find that the speed is 25 m/s and the acceleration is 250 m/s². This corresponds to row 1 in the table.

Final Answer Therefore, the correct answer is row 1.


Examples
Understanding circular motion is crucial in many real-world applications, such as designing amusement park rides or calculating the trajectory of satellites. For example, when engineers design a roller coaster, they need to consider the centripetal acceleration experienced by the riders to ensure their safety and comfort. Similarly, when launching a satellite into orbit, scientists must accurately calculate the required speed and acceleration to maintain the satellite's orbit around the Earth. These calculations rely on the principles of circular motion, making it a fundamental concept in physics and engineering.

Answered by GinnyAnswer | 2025-07-08

Approximately 2.81 x 10^21 electrons flow through the electric device delivering a current of 15.0 A for 30 seconds. This is calculated by finding the total charge using the formula Q = I × t and then dividing that charge by the charge of a single electron. The flow of electrons represents the total electric charge transported during that time period.
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Answered by Anonymous | 2025-07-10