A group of students observes that a wooden block (m = 0.40 kg) on the end of a string with a radius of 0.7 meters makes 5 rotations in 20.7 seconds when twirled.
To solve this problem, we can use the formula for the period of rotation, which is the time taken for one complete rotation. The formula is:
T = (2πr) / v
where,
T is the period of rotation,
π is a constant approximately equal to 3.14159,
r is the radius of the circular path,
v is the linear velocity of the object.
In this case, the wooden block makes 5 rotations in 20.7 seconds. We need to find the linear velocity of the block.
Linear velocity (v) can be calculated using the formula:
v = (2πrn) / T
where,
n is the number of rotations.
First, let's calculate the period of rotation (T):
T = 20.7 seconds / 5 rotations
T = 4.14 seconds/rotation
Next, we can substitute the given values into the formula for linear velocity:
v = (2π * 0.7 * 5) / 4.14
Calculating this, we find:
v ≈ 5.34 m/s
So, the linear velocity of the wooden block is approximately 5.34 m/s.