Point of support 49. A conical pendulum is formed by attaching a 500 g ball to a

Question

Point of support 49. 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 P6.49 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 1.0 m in rpm? Hint: Determine the horizontal and FIGURE P6.49 vertical components of the forces act- ing on the ball, and use the fact that the vertical component of acceleration is zero since there is no vertical motion.

Explanation / Answer

let tensions in the string be T and angular speed be w rad/s.

angle made by the string with vertical=theta=arcsin(radius/length of string)

=11.537 degrees

balancing forces in vertical direction:

T*cos(theta)=weight of the pendulum

==>T*cos(11.537)=0.5*9.8

==>T=5 N

part b:

balancing force along horizontal direction:

T*sin(theta)=mass*w^2*r

==>5*sin(11.537)=0.5*w^2*0.2

==>w=3.1626 rad/s

=30.2 rpm

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---