a.During one complete circle, starting anywhere, calculate the total work done o

Question

a.During one complete circle, starting anywhere, calculate the total work done on the ball by the tension in the string.

b.During one complete circle, starting anywhere, calculate the total work done on the ball by gravity.

c.Repeat part (a) for motion along the semicircle from the lowest to the highest point on the path

d.Repeat part (b) for motion along the semicircle from the lowest to the highest point on the path.

0.900-kg m and swung in a vertical circle. a.During one complete circle, starting anywhere, calculate the total work done on the ball by the tension in the string. b.During one complete circle, starting anywhere, calculate the total work done on the ball by gravity. c.Repeat part (a) for motion along the semicircle from the lowest to the highest point on the path d.Repeat part (b) for motion along the semicircle from the lowest to the highest point on the path. kg} ball is tied to the end of a string of length 1.70m

Explanation / Answer

As we know that work done(W) is the dot product of force vector (F) and displacement vector(s).

W = F. s or W= F*s* cosx , where x is the angle between F and s vectors

a.) During one complete circle, the ball returns back to its original position. Hence s = 0 ( displacement is zero). Thus work done is zero.

b.) Similarly as in a.) the displacement is again zero, hence the work done is zero.

c.) If the ball completes a semicircle, then displacement of ball is 2 times the radius of string as the ball will be on the diametrically opposite side of circle.

Hence displacement(s) = 2*r , r= radius of string

s = 2*1.7 = 3.4 m

At every point,The tension is string acts perependicular to the direction of motion of ball.

because the tension is along the radial direction and motion of ball is along tangential direction, hence angle between F and s = 90 degrees.

Now work done = F*s* cos 90 = 0 ( since cos90 is zero)

d.) work done by gravitational force = F* s* cos 180 ( f acts vertically downward and displacement vector s is upward from lowermost point to topmost point)

W = mg. s. (-1) = 0.9* g*3.4 * (-1) = - 0.9*10*3.4 N

W = -30.6 N

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