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.