Physics question

**milan** · May 19th 2008, 06:48 AM

The pciture shows a body of mass .24kg attached to a fixed point P by a light string of length .8m. When the body is at A, vertically below P, it is given an initial hosirontal velocity of 5m/s as shown. It then follows a circular path to the point B. When it is at B calculate:
i) The velocity of body
ii) The centripetal acceleration of the body
iii) The force exerted by the string on the body.

**o_O** · May 19th 2008, 09:06 AM

(a) Kinetic energy and potential energy is conserved so consider this at point A and at point B.

$KE_{i} + PE_{i} = KE_{f} + PE_{f}$
$\frac{1}{2}mv_{i}^{2} + mgh_{i} = \frac{1}{2}mv_{f}^{2} + mgh_{f}$

Take h = 0 at point A and notice you can cancel the m from the equation:
$\frac{1}{2}v_{i}^{2} = \frac{1}{2}v_{f}^{2} + gh_{f}$
$\frac{1}{2}(5 \text{ ms}^{-1}) = \frac{1}{2}v_{f}^{2} + (9.81 \text{ ms}^{-2})(.8 \text{ m})$

(b) $a = \frac{v^{2}}{r}$

(c) This is referring to the tension of the string and is the only thing providing the centripetal force (the only thing keeping the object in centripetal motion). So: $T = ma = \frac{mv^{2}}{r}$

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