A large box 4.5 m tall and 1.5 m wide has mass 90 kg. A horizontal force F is ap

Question

A large box 4.5 m tall and 1.5 m wide has mass 90 kg. A horizontal force F is applied as shown. The coefficient of kinetic friction is 0.25. What is the maximum height at which the force can be applied that will not tip over the box when the box slides at constant speed across the floor?

A large box 4.5 m tall and 1.5 m wide has mass 90 kg. A horizontal force F is applied as shown. The coefficient of kinetic friction is 0.25. What is the maximum height at which the force can be applied that will not tip over the box when the box slides at constant speed across the floor?

Explanation / Answer

Constant speed motion means no acceleration.

So, a = 0 m/s2

Since acceleration is 0 force applied must be equal to friction force.

Force applied = F = uMg = 0.25*90*9.8 =220.5 N

let the force is applied at height H above ground

For not to topple condition

Moment of F about centre = Moment of Friction about centre

F * (H - 4.5/2) = umg * 1.5/2

H = 1.5/2 + 4.5/2 = 3 m <-------ans

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