(a) Determine the ball\'s speed. 1 Your response differs from the correct answer

Question

(a) Determine the ball's speed.
1
Your response differs from the correct answerby 10% to 100%. m/s

(b) If, instead, the ball is revolved so that its speed is 4.0 m/s,what angle does the cord make with the vertical?
2
Your response differs from the correct answerby 10% to 100%.°

(c) If the cord can withstand a maximum tension of 9.3 N, what is the highest speed at which the ballcan move?
3
Your response differs from the correct answerby 10% to 100%. m/s

Explanation / Answer

a) we can find the tension in the string by knowing the verticalcomponent of tension must support the weight of the ball since theball is not acclerating in the vertical plane T cos 30=mg =>T=0.5kgx9.8m/s/s/cos 30 = 5.66N the horizontal component of tension is then Tsin30=2.83N and this component of tension provides the force to create thecentripetal acceleration, so we ahve Tsin30=mv^2/r => v=sqrt[r Tsin30/m] v=sqrt[1.2x2.83/0.5]=2.61m/s b) now the horizontal tension must equal T(horizontal)=mv^2/r = 0.5kgx(4m/s)^2/1.2m=6.67N the vertical component of tension must still equal the weight ofthe ball, 4.9N, so if theta is the angle made with the vertical, wehave tan(theta)=T(hor)/T(vert)=6.67/4.9=>th… c) assume the string is horizontal and does not need to support theweight of the ball; then the greatest speed is T=mv^2/r => v=sqrt[r T/m] = sqrt[1.2 m x 9.5N/0.5kg] v=4.78m/s

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