1. ## physics forces

A trolley filled with sand moves with a velocity , u on a smooth horizontal surface . At time , t=0 , sand starts to fall vertically at a constant rate from a hole at the centre of the base of the trolley . When time t=T , all the sand has fallen out .

The graph from the book shows that the trolley's velocity is constant all the way . Shouldn't the acceleration be increasing since the mass of trolley is decreasing from F=ma .

Or maybe it is because of the nature of the surface (smooth) . I am a bit confused here although it seems simple . Thanks.

2. I assume you mean frictionless surface - so no forces are acting on the trolley.
The mass of the trolley is decreasing, yes. But an acceleration requires a force, and no forces act upon it. Therefore there is no change in acceleration.
The velocity remains the same also. Momentum is conserved because the sand that falls out still has a horizontal velocity. If the surface is indeed frictionless, then the sand that falls out would continue moving along the surface underneath the trolley. The sand hitting the surface would stop its Y velocity but not its X velocity.

3. Originally Posted by Marth
I assume you mean frictionless surface - so no forces are acting on the trolley.
The mass of the trolley is decreasing, yes. But an acceleration requires a force, and no forces act upon it. Therefore there is no change in acceleration.
The velocity remains the same also. Momentum is conserved because the sand that falls out still has a horizontal velocity. If the surface is indeed frictionless, then the sand that falls out would continue moving along the surface underneath the trolley. The sand hitting the surface would stop its Y velocity but not its X velocity.

thanks a lot marth , clear explaination .