A pendulum of length 55 cm swings through an angle of 16 degrees. What distance does the tip of the pendulum swing?
s = rθ
you have r and θ, so plug them in (θ in radians). That will give you the actual arc length traveled.
If you want the horizontal distance, assuming symmetry, then you will need
x/2 = r sin(θ/2)
To find the distance that the tip of the pendulum swings, we need to compute the arc length of the swing.
The arc length, denoted by s, can be calculated using the formula:
s = θr
Where θ is the angle in radians and r is the radius of the circle, which is equal to the length of the pendulum.
First, we need to convert the angle from degrees to radians. We know that 180 degrees is equal to π radians, so we can set up a proportion:
180 degrees = π radians
16 degrees = x radians
To solve for x, we can cross multiply and divide:
16 * π radians = 180 * x radians
16π = 180x
x = (16π) / 180
Now that we have the angle in radians, we can substitute the values into the formula:
s = (16π / 180) * 0.55
Calculating the value, we get:
s ≈ 0.919 meters
Therefore, the distance that the tip of the pendulum swings is approximately 0.919 meters.