the pendulum of a grandfather clock is 1.3m long. Determine the length of the arc through which the pendulum moves if it moves through an angle of 15
circumference of the potential whole circle = 2π(1.3)
= 2.6π
so , by a simple ratio
arc/2.6π = 15/360
arc = 2.6π(15/360) = (13/120)π or appr .34 m
or 34 cm
To determine the length of the arc through which the pendulum moves, we can use the formula for the arc length of a pendulum:
Arc Length = (Pendulum Length) * (Central Angle in Radians)
In this case, the pendulum length is given as 1.3 meters, and the central angle is 15 degrees. However, we need to convert the angle to radians before plugging it into the formula.
To convert degrees to radians, we use the formula:
Radians = (Degrees * π) / 180
Let's calculate the radians first:
Radians = (15 * π) / 180
= (15π) / 180
= π/12
Now we can calculate the arc length using the formula:
Arc Length = (Pendulum Length) * (Central Angle in Radians)
= 1.3 * (π/12)
≈ 0.3416 meters (rounded to four decimal places)
Therefore, the length of the arc through which the pendulum moves is approximately 0.3416 meters.
To determine the length of the arc through which the pendulum moves, we can use the formula:
Arc Length = Radius * Angle
In this case, the length of the pendulum is given as 1.3m, which is the radius of the arc. The angle through which the pendulum moves is given as 15 degrees.
To use this formula, we need to convert the angle from degrees to radians, as the formula requires the angle to be in radians.
To convert the angle from degrees to radians, we use the conversion factor: π/180. So, the angle in radians can be calculated as:
Angle (in radians) = Angle (in degrees) * π/180
Let's calculate the angle in radians:
Angle (in radians) = 15 * π/180
Angle (in radians) = 0.2618 radians (approximately)
Now, plug the values into the formula:
Arc Length = Radius * Angle
Arc Length = 1.3m * 0.2618 radians
Arc Length ≈ 0.33934 meters
Therefore, the length of the arc through which the pendulum moves is approximately 0.33934 meters.