Posted by **LEBZA** on Monday, April 2, 2012 at 4:20am.

A minimum horizontal force of 10 N is needed to keep a 500 g book in place against a wall as shown.What maximum mass of book could be supported by the 10 N force if it were directed upwards at an angle of 60° instead of at right angles to the wall?

- Physics -
**Elena**, Monday, April 2, 2012 at 11:10am
When the force F is normal to the wall the projections of the forces acting on the book are

x: N = F,

y: mg =F(fr).

F(fr) = k•N = k•F,

k•F = m•g,

k = m•g/F =0.5•9.8/10 = 0.49.

When the force F is at 60o to horizontal the projections of the forces acting on the book are

x: N1 = F•cosα

y: m1•g =F(fr)+F•sinα

F(fr) = k•N1= k•F•cosα,

F(fr) = m1•g - F•sinα,

k•F•cosα= m1•g - F•sinα,

m1=F•( k• cosα +sinα)/g =

= 10(0.49•0.5 + 0.866)/9,8 = 1.13 kg.

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