p13 060

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60. Since all surfaces are frictionless, the contact force 

F exerted by the lower sphere on the upper one is

along that 45

line, and the forces exerted by walls and floors are “normal” (perpendicular to the wall

and floor surfaces, respectively). Equilibrium of forces on the top sphere lead to the two conditions

N

wall

= F cos 45

and

F sin 45

= mg .

And (using Newton’s third law) equilibrium of forces on the bottom sphere lead to the two conditions

N



wall

= F cos 45

and

N



floor

= F sin 45

+ mg .

(a) Solving the above equations, we find N



floor

= 2mg.

(b) Also, we obtain N



wall

= N

wall

= mg.

(c) And we get F = mg/ sin 45

= mg

2.


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