The document discusses the forces acting on two spheres stacked on top of each other on a frictionless surface. It states that the contact force between the spheres is at a 45 degree angle. Applying equilibrium conditions for the forces on each sphere yields equations relating the normal forces from the wall and floor to the contact force and gravitational force. Solving these equations shows that the normal force from the floor is 2mg, the normal forces from the wall are mg, and the contact force between the spheres is mg√2.

1. 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
Nwall = 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
Nwall = F cos 45◦ and Nfloor = F sin 45◦ + mg .
(a) Solving the above equations, we find Nfloor = 2mg.
(b) Also, we obtain Nwall = Nwall = mg.
√
(c) And we get F = mg/ sin 45◦ = mg 2.