When the string is pulled a distance of 40 cm in 2.50 s, the wheel turns though 5 revolutions. What is the average speed of the string, and what is the average angular velocity of the wheel? What is the radius of the wheel?
To find the average speed of the string, we need to divide the distance traveled by the time taken. In this case, the distance traveled by the string is 40 cm and the time taken is 2.50 s. Therefore, the average speed of the string can be calculated as follows:
Average speed = Distance / Time = 40 cm / 2.50 s = 16 cm/s
So, the average speed of the string is 16 cm/s.
To find the average angular velocity of the wheel, we need to consider the number of revolutions and the time taken. In this case, the wheel turns through 5 revolutions and the time taken is 2.50 s. We know that 1 revolution is equal to 2π radians. Therefore, we can calculate the average angular velocity of the wheel as follows:
Average angular velocity = (Number of revolutions * 2π) / Time = (5 * 2π) / 2.50 s
To calculate the average angular velocity, we need to know the value of π (pi). π is approximately equal to 3.14. Substituting this value into the equation:
Average angular velocity = (5 * 2 * 3.14) / 2.50 s = 31.4 rad/s
So, the average angular velocity of the wheel is 31.4 rad/s.
To find the radius of the wheel, we can use the formula for the circumference of a circle:
Circumference = 2πr
In this case, we know that the wheel turns through 5 revolutions, which means the circumference of the wheel is covered 5 times. Therefore:
5 * Circumference = Distance traveled by the string = 40 cm
Substituting the formula for the circumference:
5 * (2πr) = 40 cm
Simplifying the equation:
10πr = 40 cm
Dividing both sides by 10π:
r = 40 cm / (10π)
Approximating π to 3.14:
r = 40 cm / (10 * 3.14) ≈ 1.27 cm
So, the radius of the wheel is approximately 1.27 cm.