A pendulum is105 long and swing about one end through 5degree on either side of the vertical.one complete swing takes 2seconds back to the starting point.1 through what angle does he pendulum swing in one complete swing?
2 how far does the tip of the pendulum travel in 1 hour
#1. 5+5 = 10
#2. 105*(10 * π/180)*(3600/2)
To find the answers to these questions, we can use some basic principles of physics and trigonometry. Let me explain step by step:
1. Angle of swing:
In one complete swing of a pendulum, it starts from its initial position, swings to one side, swings back to the other side, and returns to the starting point.
Given that the pendulum swings 5 degrees on either side of the vertical, the total angle covered in one complete swing is 5 degrees + 5 degrees = 10 degrees.
Therefore, the pendulum swings through an angle of 10 degrees in one complete swing.
2. Distance traveled by the tip of the pendulum in 1 hour:
We know that the pendulum takes 2 seconds to complete one swing and return to the starting point. Let's calculate the distance traveled by the tip of the pendulum in one swing first.
To find this distance, we need to consider the length of the pendulum and the angle of swing.
Using trigonometry, we can determine that the distance covered by the tip of the pendulum in one swing is given by:
Distance = 2 * length * sin(angle/2)
Given:
Length of the pendulum (L) = 105 cm
Angle of swing (θ) = 10 degrees
Converting the angle from degrees to radians:
θ (in radians) = θ (in degrees) * π / 180
θ (in radians) = 10 degrees * π / 180
θ (in radians) = 0.1745 radians
Now, substituting the values into the formula:
Distance = 2 * 105 cm * sin(0.1745 radians)
Distance ≈ 2 * 105 cm * 0.1736
Distance ≈ 36.372 cm (approximately)
Therefore, the tip of the pendulum travels approximately 36.372 cm in one swing.
To find the distance traveled in 1 hour, we need to find the number of swings the pendulum completes in 1 hour and multiply that by the distance traveled in one swing.
Number of swings in 1 hour = 3600 seconds / (2 seconds per swing) = 1800 swings
Distance traveled in 1 hour = 1800 swings * 36.372 cm per swing
Distance traveled in 1 hour ≈ 65,469.6 cm or 654.696 meters (approximately)
Therefore, the tip of the pendulum travels approximately 654.696 meters in 1 hour.
1. To find the angle that the pendulum swings in one complete swing, we can use the given information that it swings about one end through 5 degrees on either side of the vertical. Since it swings on either side, the total angle covered in one complete swing is twice that amount.
Total angle = 2 * (5 degrees)
Total angle = 10 degrees
Therefore, the pendulum swings through an angle of 10 degrees in one complete swing.
2. To find how far the tip of the pendulum travels in 1 hour, we need to calculate the distance covered in each swing and then find the number of swings in 1 hour.
The distance covered in one swing can be calculated using the length of the pendulum and the angle it swings.
Distance covered in one swing = 2 * pi * (length) * (swing angle / 360 degrees)
Distance covered in one swing = 2 * 3.14 * 105 * (10 degrees / 360 degrees)
Distance covered in one swing ≈ 11.57 inches (rounded to two decimal places)
Since one complete swing takes 2 seconds, the pendulum will make 1/2 a swing in 1 second (since half the swing is covered in 1 second). Therefore, the number of swings in 1 hour can be calculated as:
Number of swings = (3600 seconds in 1 hour) / (2 seconds per swing)
Number of swings = 1800 swings
The total distance covered by the tip of the pendulum in 1 hour can be calculated as:
Total distance = Distance covered in one swing * Number of swings
Total distance ≈ 11.57 inches * 1800
Total distance ≈ 20,826 inches (rounded to two decimal places)
Therefore, the tip of the pendulum travels approximately 20,826 inches in 1 hour.