Sloped Bed Truck: Acceleration & Normal Force?

[QuantumKing]

If I have a truck with a sloped bed in the back, the truck is accelerating horizontally and there's a block sitting on the slope tied to a rope while all this is happening. I was wondering if the trucks acceleration would cause the normal force being applied to the block by the sloped bed to diminish?

Thanks

 

[Shooting Star]

Certainly. If x is the angle between the slope and the horizontal, then initially the normal reaction was mg*cos x. If ‘a’ is the accn of the truck, then the diminished normal reaction is mg*cos x –ma*sin x. Note that the normal reaction could become zero if ‘a’ is high enough. Negative value means that the block is no more resting on the slope because the truck is accelerating so fast.

One way of calculating forces on static objects in accelerating frames is to think that there is an effective gravity of '–a' in that frame, on top of any actual gravity.

 

[charng]

for your question. I can assure you that the acceleration of the truck will have an effect on the normal force applied to the block on the sloped bed. This is because the normal force is dependent on the weight of the block and the angle of the slope. As the truck accelerates, the weight of the block remains constant, but the angle of the slope changes due to the horizontal motion of the truck. This change in angle will result in a change in the normal force applied to the block.

To better understand this concept, let's break down the forces acting on the block on the sloped bed. Firstly, we have the weight of the block, which is the force pulling the block downwards due to gravity. This weight is counteracted by the normal force, which is equal in magnitude but opposite in direction. The normal force is essentially the force exerted by the surface of the sloped bed on the block to prevent it from sinking into the surface.

Now, as the truck accelerates horizontally, the block will experience a horizontal force due to its inertia. This force will act in the opposite direction of the truck's acceleration. This means that the block will want to slide down the slope, and the normal force will have to increase to prevent this from happening.

In summary, the truck's acceleration will cause the normal force applied to the block to increase, not diminish. This is because the angle of the slope will change, requiring a greater normal force to keep the block in place. I hope this explanation helps to clarify your question.