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enter image description here

Simplified the question. Now if anybody can kindly explain the FBD for direction of normal force.

PS: do not need the solution to problem of roller curb at a step but how the Normal force at A is pointed toward the point of application of force and not toward the center of roller

Sage
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2 Answers2

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A rigid body is rigid because it pushes back when you push on it. This push back is the reaction force. The body pushes back just hard enough to keep you from pushing into the body.

For a flat surface like your first picture, the reaction force is perpendicular to the surface. Any sideways force is friction. Friction prevents or opposes two surfaces sliding past each other. This is different from penetrating into each other.

Typically, you figure out how strong a reaction force is by how strong other forces are. Gravity pulls the roller down with force $mg$. The reaction force is just strong enough to prevent this. The roller has no downward acceleration. The total vertical force is $0$. The magnitude of the reaction force must also be $mg$.

The reaction force is the same if the surface is made of ice. The roller can slide sideways freely. But it can't penetrate into the ice.

Even thought there is no perpendicular direction at the step, you can apply these ideas to figure out the direction of the reaction force.

When the roller contacts the step, which direction would cause it to penetrate into the step and which would allow the roller to move without distortion. The roller can rotate around the point of contact, but not decrease the distance from the center of the roller to the step.

There are tension and gravity forces that try to push the roller. You can resolve it into a component in the forbidden direction and perpendicular to that direction. The reaction force opposes motion in the forbidden direction.

mmesser314
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I think have resolved my own query. For anybody else for a static system we can generalize if >=2 forces are acting then normal force is direction towards the point of intersection of the forces and thus if point of application is at center of roller, then normal force is towards the center of roller which happens to be also the point of application of force. as depicted. enter image description here as if >=2 forces are acting in static equilibrium then forces have to be concurrent or parallel. in each of the case assume the static equilibrium state with only contact at A.

Sage
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