A ball on a 1.4-meter long string is being whirled in mid-air in a horizontal circle at a
constant speed v. The tension in the string is 100 N. The mass of the ball is 3.70 kg.
What is v?
Use DID TASC
Step 1: Diagram & coordinate system. Choose +x radially inward & +y vertically up.
Steps 2 & 3: Isolate. Draw Forces (see transparency).
Step 4: Take components.
Tx = T cos θ Ty = T sinθ
Step 5: Apply Newton's Second Law for each component:
y-component ΣFy = may = 0 gives T sin θ = mg
x-component ΣFx = max gives T cos θ = m v2/r
Important: Here r is the radius of the circle! and not the string length.
Step 6: Solve.
y-equation: With T = 100 N and mg = 36.26 N, θ = 21.26 degrees.
Neat! Divide the y-equation by the x-equation: tan θ = g r/v2.
Either the x-equation or the neat relation then gives the speed.
Use r = 1.40 cos θ = 1.305 m, we obtain v
= 5.73 m/s.