How Do You Calculate Tension and Pole Force on a Leaning Tether Ball?

[Edwardo_Elric]

Homework Statement

A tether ball leans against the post to which it is attached. If the string to which the ball is attached is 1.80m long, the ball has a radius of .200m, and the ball has a mass of .500kg, what are the tension in the rope and the force the pole exerts on the ball? assume that there is so little friction between the ball and the pole that it can be neglected. ( The string is attached to the ball such that a line along the string passes through the center of the ball.)

Homework Equations

$$F_{x} = 0$$
$$F_{y} = 0$$

The Attempt at a Solution

Part I
Required: tension on the rope
T = ??
wball = (.500kg)(9.8m/s^2) = 4.9N
$$\sum{F_{y}} = 0 = T\cos{\theta} + (-w_{ball})$$
$$T = \frac{4.9N}{\cos{\theta}}$$
*I computed theta using its distances:
sin(theta) = x_{radius} / h_{tension}
= arcsin {0.200m/1.80m}
= 6.38 degress
$$T = \frac{4.9N}{\cos{6.38}}$$

T =4.93N

Part II
reqd: force on pole on ball:
F_{pole on ball} = ?
\sum{F_{x}} = 0 = T\sin{\theta} - F_{p.on.B}
(4.93N)sin{6.38} = F_{pole on ball}
F = .548N?

 

[andrevdh]

You've got both answers correct.