In the figure below a uniform sphere of mass m 085 kg and r

In the figure below, a uniform sphere of mass m = 0.85 kg and radius r = 1.8 cm is held in place by a massless rope attached to a frictionless wall a distance L = 10.4 cm above the center of the sphere. What is the tension in the rope? What is the force on the sphere from the wall? Draw an xy coordinate system. Draw the forces on the sphere. Do you see that there are there? Write A balance-of-force equation for the vertical y axis. Do ypu recall that you should use only the vertical force component? Do you also recall how to find a component of a vector from the magnitude and angle? What is the acceleration? Next, write A balanced-of-forces equation for the horizontal x axis.

Solution

From Newtons 2nd law, Vertical component

TCos(a)-mg=0

T=mg/Cos(a)

From Figure

Cos(a) =r/sqrt[L²+r²] =1.8/sqrt[1.8²+10.4²] =0.17

So Tension in the rope

T=0.85*9.8/0.17

T=48.84 N