Question

Young David, who slew Goliath, experimented with slings before tackling the giant. He found that he could revolve a sling of length 0.600 m at the rate of 8.00 rev/s. If he increased the length to 0.900 m, he could revolve the sling only 6.00 times per second.

(a) Which rate of rotation gives the greater speed for the stone at the end of the sling?

A. 8.00 rev/s
B. 6.00 rev/s
C. Both rates result in the same speed
D. It cannot be determined

Answer 1

The greater speed for the stone at the end of the sling is achieved with the sling rotating at 6.00 rev/s with a length of 0.900 m, which results in a speed of 33.93 m/s.

Step-by-step explanation:

The student is asking which rate of rotation gives the greater speed for the stone at the end of David's sling between 8.00 revolutions per second (rev/s) with a 0.600 m sling length and 6.00 rev/s with a 0.900 m sling length. The speed of an object in circular motion is given by the equation speed = 2π * radius * frequency, where the radius is the length of the sling and the frequency is the rate of rotation in rev/s.

For the first case with a sling length of 0.600 m at 8.00 rev/s, the speed is:

v1 = 2π * 0.600 m * 8.00 rev/s = 30.16 m/s

For the second case with a sling length of 0.900 m at 6.00 rev/s, the speed is:

v2 = 2π * 0.900 m * 6.00 rev/s = 33.93 m/s

Therefore, the greater speed for the stone is achieved with the sling rotating at 6.00 rev/s (Option B).