Say you want to make a sling by swinging a mass M of 1.9 kg in a horizontal circle of radius 0.042 m, using a string of length 0.042 m. You wish the mass to have a kinetic energy of 15.0 Joules when released. How strong will the string need to be? (How much tension will there be in the string?)

Question

Physics

Abbott

Today, 02:55

Say you want to make a sling by swinging a mass M of 1.9 kg in a horizontal circle of radius 0.042 m, using a string of length 0.042 m. You wish the mass to have a kinetic energy of 15.0 Joules when released. How strong will the string need to be? (How much tension will there be in the string?)

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Answers (1)

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Nash · Answer 1

Answer: T = 715 N

Explanation:

The only external force (neglecting gravity) acting on the swinging mass, is the centripetal force, which. in this case, is represented by the tension in the string, so we can say:

T = mv² / r

At the moment that the mass be released, it wil continue moving in a straight line at the same tangential speed that it had just an instant before, which is the same speed included in the centripetal force expression.

So the kinetic energy will be the following:

K = 1/2 m v² = 15. 0 J

Solving for v², and replacing in the expression for T:

T = 1.9 Kg (3.97) ² m²/s² / 0.042 m = 715 N