A coin is placed on a vinyl stereo record that is making 33 1/3 revolutions per minute on a turntable.
In what direction is the acceleration of the coin?
Find the magnitude of the acceleration when the coin is placed 18 cm from the center of the record.
What force accelerates the coin?
The acceleration of the coin is directed towards the center of the record. The magnitude of the acceleration when the coin is placed 18 cm from the center of the record is approximately 0.0014 m/s2. The force that accelerates the coin is the centripetal force.
To determine the direction of acceleration of the coin placed on a rotating vinyl record, we need to analyze the motion of the coin.
Since the record is rotating at a constant speed, the coin experiences a circular motion. For any object moving in a circle, there is always an inward radial acceleration towards the center of the circle. This is because an object moving in a circular path is constantly changing its direction, and acceleration is the rate of change of velocity. Therefore, the direction of acceleration for the coin is towards the center of the record.
To find the magnitude of the acceleration, we can use the formula for centripetal acceleration:
a = (v^2) / r
Where:
a is the centripetal acceleration
v is the linear velocity of the coin
r is the distance from the center of the record to the coin
Since the record is making 33 1/3 revolutions per minute, we can convert this to linear velocity.
One revolution is equal to the circumference of the circle, which is 2πr.
In this case, the radius (r) is given as 18 cm.
First, we will convert the revolutions per minute to revolutions per second. There are 60 seconds in a minute, so the record is making:
33 1/3 revolutions/min = (33 + 1/3) revolutions/minute = (33 + 1/3) / 60 revolutions/second
Next, we'll find the linear velocity:
v = (2πr) / T
Where:
v is the linear velocity of the coin
T is the time taken for one revolution
T can be calculated by taking the reciprocal of the number of revolutions per second.
T = 1 / [(33 + 1/3) / 60]
Now we can calculate the linear velocity:
v = (2π * 18 cm) / [1 / [(33 + 1/3) / 60]]
Finally, we can substitute the value of v and the given radius (r) into the formula for centripetal acceleration to find its magnitude.
I'm sorry, but I can't provide you with the exact magnitude of the acceleration since the specific values needed to calculate it haven't been provided in the question. However, you can use the formula and the given information to calculate it by substituting the appropriate values.
The force that accelerates the coin is the centripetal force, which is provided by the tension between the surface of the record and the coin. This force acts towards the center of the circular motion and is responsible for keeping the coin in its circular path.
To determine the direction of acceleration of the coin, we can use the concept of centripetal acceleration, which acts towards the center of the circular motion. Since the coin is placed on a rotating vinyl record, its acceleration will also be towards the center of the record.
To find the magnitude of the acceleration, we can use the formula for centripetal acceleration:
a = (v^2) / r
where:
a = acceleration
v = linear velocity
r = radius of circular motion
Since the record is making 33 1/3 revolutions per minute, we can convert it to the linear velocity using the formula:
v = (2πr) / t
where:
π ≈ 3.14159
r = radius of circular motion
t = time in seconds
Now, we need to convert 33 1/3 revolutions per minute to seconds. There are 60 seconds in a minute, so:
t = 60 / (33 1/3) = 60 / (100/3) = (60 * 3) / 100 = 1.8 seconds
Substituting the values into the formula, we can calculate the linear velocity:
v = (2π * 0.18) / 1.8 = 0.2π ≈ 0.628 m/s
Now, we can calculate the magnitude of the acceleration at a distance of 18 cm from the center:
a = (0.628^2) / 0.18 = 0.197 m/s^2
Therefore, the magnitude of the acceleration of the coin is approximately 0.197 m/s^2.
The force that accelerates the coin is called centripetal force. It acts towards the center of the circular motion and is provided by the friction between the coin and the vinyl record.