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Physics question
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.

(a) Kinetic energy and potential energy is conserved so consider this at point A and at point B.
$\displaystyle KE_{i} + PE_{i} = KE_{f} + PE_{f}$
$\displaystyle \frac{1}{2}mv_{i}^{2} + mgh_{i} = \frac{1}{2}mv_{f}^{2} + mgh_{f}$
Take h = 0 at point A and notice you can cancel the m from the equation:
$\displaystyle \frac{1}{2}v_{i}^{2} = \frac{1}{2}v_{f}^{2} + gh_{f}$
$\displaystyle \frac{1}{2}(5 \text{ ms}^{1}) = \frac{1}{2}v_{f}^{2} + (9.81 \text{ ms}^{2})(.8 \text{ m})$
(b) $\displaystyle a = \frac{v^{2}}{r}$
(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: $\displaystyle T = ma = \frac{mv^{2}}{r}$