A mass tied to a string and whirled in a circle of radius 0.5m, if m=2kg and speed of motion is 2m/s.?

Question by Mc: A mass tied to a string and whirled in a circle of radius 0.5m, if m=2kg and speed of motion is 2m/s.?
A.) What is the acceleration of the mass?

B.) What is the tension in the string?

Best answer:

Answer by John Stevens
a=v^2/r
a=(2^2)/.5
a=8 m/s^2
F=ma
F=2*8=16 N

Know better? Leave your own answer in the comments!

2 comments to A mass tied to a string and whirled in a circle of radius 0.5m, if m=2kg and speed of motion is 2m/s.?

  • E  says:

    What John Stevens means, of course, is

    a=v^2/r
    a=(2 m/s)² / (0.5 m)
    a=8 m/s²
    F=ma
    F=(2 kg)*(8 m/s²)=16 N

    because something like

    F = 2*8 = 16 N

    would be nonsense. The product of two unitless numbers can’t be a force.

    ****************

    Edit: But what JullyWum means is even better, assuming the circle is horizontal and there’s nothing else supporting the mass.

  • JullyWum  says:

    Centripetal acceleration .. a = v² / R .. .. (2.0m/s)² / 0.50m .. .. .. ?a = 8.0 m/s²

    Due to the weight of the mass (mg), the string is at an angle below the horizontal.

    The vertical component of the tension supports the weight ..
    Tv = mg .. 2.0kg x 9.80N/kg .. .. Tv = 19.60N
    The horiz. component of the tension provides the centripetal force ..
    Th = m.v²/R .. 2.0kg x 8.0m/s² .. .. Th = 16.0N

    T² = Tv² + Th² .. 19.6² + 16.0² = 640.20 .. .. T = ?640 .. .. .. ?T = 25.30N

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