A pendulum has a mass of 3-kg, a length of 2 meters and swings through a (half)arc of 27.3 degrees. What is its Amplitude to the nearest centimeter ?
Yeah too bad I've never taken trig and have no idea what half-arc even means
How do you define amplitude in this case? It could be height range L(1-cos27.3), sideways motion range (L sin 27.3) or angle range (27.3 degrees). Once you have the definition, use the half-arc angle and trigonometry.
The angle range would not have units of length, so it isn't that.
The mass does not affect the answer.
Well it's a bit too late for that. I'm already in Calc 2 so is there anyway you can just explain this problem to me so I can finish my work.
To find the amplitude of a pendulum, we first need to understand what it represents. The amplitude of a pendulum is the maximum displacement from its equilibrium position (the vertical position in the middle of its swing). It is the distance from the equilibrium position to the point where the pendulum reaches its highest swing on one side.
To calculate the amplitude, we can use the following formula:
Amplitude = Length × sin(ang)
Where:
- Length is the length of the pendulum (given as 2 meters)
- ang is the angle through which the pendulum swings (given as 27.3 degrees)
First, we need to convert the angle from degrees to radians because the sine function in the formula takes radians as input. To convert degrees to radians, we use the following formula:
radians = degrees × (π/180)
So, let's calculate the radians:
radians = 27.3 × (π/180)
Now, we can calculate the amplitude:
Amplitude = 2 × sin(radians)
After getting the value of the amplitude, we can round it to the nearest centimeter. Let's calculate it using a calculator or programming language:
Amplitude ≈ 2 × sin(0.476) ≈ 2 × 0.456 ≈ 0.912 meters
To convert the amplitude from meters to centimeters, we multiply it by 100:
Amplitude ≈ 0.912 × 100 ≈ 91.2 centimeters
So, the amplitude of the pendulum is approximately 91.2 centimeters (rounded to the nearest centimeter).
The half arc is the maximum angle swing, in this case 27.3 degrees.
You should not be taking physics if you haven't had trigonometry