Two boxes with mass m and M are on an incline as shown. The incline makes angle

Question

Two boxes with mass m and M are on an incline as shown. The incline makes angle 0 with the horizontal direction. A Force F is applied on the box with mass M in the horizontal direction.

i) Determine the contact force between the two boxes

ii) What is the acceleration of the system?

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Problem 3 Two boxes with mass m and M are on an incline as shown. The incline makes angle o with the horizontal direction. A Force F is applied on the box with mass M in the horizontal direction. Determine the contact force between the two boxes. ii) What is the acceleration of the system Figure 4.39: Problem 3

Explanation / Answer

Component of force F acting parallel to surface on mass system will be Fcoso . Gravitational force acting on mass system in downward direction parallel to surface will be (M+m) gsino .So net force on mass system parallel to surface in upward direction will be Fcoso -(M+m)gsino . Applying Newton's law of motion , acceleration a of mass system = Fcoso -(M+m) gsino /(M+m).

This is answer of part (2)

If R be the contact force between m and M it will act on m in upward direction and on M in downward direction parallel to surface.Considering total force acting only on m , net force on it will be R- mgsino.Applying Newton's law on m we have

R-mgsino = ma =m[Fcoso- (M+m)gsino] /(M+m)

R= mgsino + m[Fcoso-(M+m)gsino]/(M+m)

= mgsino+mFcoso /(M+m) -mgsino

= mFcoso/(M+m)

This is answer of part (1)

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