a child twirls a yo-yo about in a horizontal circle. The yo-yo has a mass of 0.20 kg and is attached to a string 0.8 m long. what is the velocity of the yo-yo? thanks!
To find the velocity of the yo-yo, we can use the formula for the speed of an object undergoing circular motion. The speed of an object moving in a circle is given by the equation:
v = (2 * π * r) / T
Where:
v is the velocity of the object
π is a mathematical constant approximately equal to 3.14159
r is the radius of the circular path
T is the time taken to complete one revolution around the circle
In this case, the yo-yo is attached to a string with a length of 0.8 m, which is equal to the radius of the circular path. We need to determine the time taken for the yo-yo to complete one revolution around the circle.
The time taken for one complete revolution is called the period (T) and can be found using the equation:
T = 2 * π * sqrt(r / g)
Where:
sqrt() represents the square root function
g is the acceleration due to gravity, which is approximately 9.8 m/s^2
Let's substitute the given values into the equation to find T:
T = 2 * π * sqrt(0.8 / 9.8)
T ≈ 2 * π * 0.284
T ≈ 1.789 seconds (rounded to three decimal places)
Now that we have the period, we can calculate the velocity (v) using the first equation:
v = (2 * π * r) / T
v = (2 * π * 0.8) / 1.789
v ≈ 2.248 m/s (rounded to three decimal places)
So, the velocity of the yo-yo is approximately 2.248 m/s.