A ?conical pendulum is formed by attaching a 500 g ball to a 1.0-m-long string, then allowing the mass to move in a horizontal circle of radius 20 cm. Figure 49 shows that the string traces out the surface of a cone, hence the name. a. What is the tension in the string? b. What is the ball’s angular velocity, in rpm? Hint: Determine the horizontal and vertical components of the forces acting on the ball, and use the fact that the vertical component of acceleration is zero since there is no vertical motion. FIGURE 49

Solution Step 1 of 6 Mass of the ball, m = 500g 3 3 Using 1 g = 10 kg m = 500×10 kg =0.5 kg Radius of the circular path, r= 20 cm 2 2 Using 1 cm = 10 m r= 20 ×10 m=0.2 m Length of the string, L= 1m Step 2 of 6 The tension on the string is deduced to its components as shown in the figure below, Here the tension T = T sin+ T cos The angle made with the vertical is, = sin (1 opposite sid) hypotenuse 1 = sin ( length 1 0.2m = sin ( 1m ) = 11.5369 o Step 3 of 6 The vertical component of tension will be equal to the weight or the gravitational force. Also the horizontal component of T will equal to the centripetal force. That is Horizontal component T sin=F = cr ………….1 And vertical component T cos =F = mg…………..2 G Where m is the mass of the ball, Fcand F G is the centripetal and gravitational force.