Question

g A 1.20-kg ball is tied to a 1.20-m long string is being spun in a vertical circle at a constant speed and with a period of 1.60 is. What is the maximum tension in the string

Answer 1

T = 17.42 N

Step-by-step explanation:

angular velocity(ω) can be calculated from the expression:

=
`(2 \pi )/(T)`

Since T = 1.60

Then ω =
`(2 \pi )/(1.60)`

ω = 3.930 rad/s

Maximum tension of the string would be at the lowest point of the circle which can be written as:

T - mg = mrω ²

T = mg + mrω ²

T = m ( g + rω ²)

T = 1.2(9.8 + 1.20×3.930)

T = 17.4192 N

T = 17.42 N

Answer 2

33.94 N

Step-by-step explanation:

The maximum tension in the string,

F-mg = mω²r ..................... Equation 1

Where F = maximum tension in the string, ω = angular velocity, m = mass the ball, r = radius of the circle/length of the string. g= acceleration due to gravity

But,

ω = 2π/T................... Equation 2

Where T = Period.

Substitute equation 2 into equation 1

F = [mr(2π)²/T²]+mg............. Equation 3

Given: m = 1.2 kg, r = 1.2 m, T = 1.6 s, π = 3.14, g = 9.8 m/s²

Substitute into equation 3

F = [1.2(1.2)(4×3.14²)/1.6²]+1.2(9.8)

F = 22.18+11.76

F = 33.94 N

Hence the maximum force tension in the string = 33.94 N