Question

24. A 27-kg ball is tied to one end of a massless string of length 1.3 m. The other end of the string is tied to a nail in the center of a table. The

ball is set into uniform circular motion around the nail, and it completes one revolution every 5.2 seconds. What is the tension in the
string?
51N
44N
71N
30 N

Answer 1

51 N

Step-by-step explanation:

The circumference of the circular path is:

C = 2πr

C = 2π (1.3 m)

C = 8.17 m

The ball travels 1 circumference in 5.2 seconds, so its speed is:

v = C / t

v = 8.17 m / 5.2 s

v = 1.57 m/s

Sum of the forces on the ball in the radial direction:

∑F = ma

T = m v² / r

T = (27 kg) (1.57 m/s)² / (1.3 m)

T = 51 N

Answer 2

Answer: 51N

Explanation: T = mv^2/r 51 = 76v^2/1.3 v =.934