Q. Three identical spheres of mass M are kept touching each other,as they lie on rough ground.The friction between the spheres is negligible.

a) Draw the free body diagram of each sphere.

b) Draw the free body diagram of each sphere if a small horizontal force F is applied on the bottom left sphere along the centre line of the sphere.

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See picture below for both cases.

1. FIRST CASE

On sphere 1 there are the following forces:

G =2*N1*cos(30) weight of sphere

2 normal reactions N1 from the contact points with spheres 2 and 3

On sphere 2 and 3 there are the following forces:

G weight of each sphere

one normal reaction N2 for each sphere weight from the ground G

there is no friction force on either sphere because the horizontal components of N1 on sphere 1 cancel each other.

2. SECOND CASE (there is no friction between spheres)

On sphere 1 there are the following forces:

G the weight of sphere

2 equal normal reactions N1 from each sphere 2 and 3

G =2*N1*cos(30)

On sphere 2 there are the following forces:

G the weight of the sphere

F the applied force

N2 =G+N2*cos(30) normal reaction from the ground

N3 normal reaction from sphere 3 (at the contact point with sphere 3)

N4 normal reaction from sphere 1 (at the contact point with sphere 1)

Ff2 - friction force on the ground

Ff2 = miu*N2

On sphere 3 there are the following forces

G the weight of the sphere

N5 - normal reaction from the ground

Ff3 - Friction force on the ground

Ff3 = miu*N3

On overall on the horizontal axis for spheres 2 and 3

F + Ff2 =N3 + N5 +N4*sin(30)

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