# No resultant force means no external force?

1. Mar 7, 2009

### makeAwish

Hmm. I'm quite confused with this:
Does no resultant force means no external force?
i.e. if there is an external force, there is a resultant force?

Like say, sand falls onto a moving conveyor belt at the rate of 5.00 kg/s. The conveyor belt is supported by frictionless rollers and moves at a constant speed of 0.750m/s under the action of a constant horizontal external force Fext supplied by the motor that drives the belt.

so the friction force is the force required for the sand to move at same speed as the belt right? then can i say there is no resultant force acting on the sand?

anyway i duno if this is considered as h/w qns.. sorry.

2. Mar 7, 2009

### Staff: Mentor

Not at all. Consider a book sitting on your desk. The net force is zero, yet both gravity and the desk exert forces (external forces) on the book.

Note that the sand must be accelerated from zero speed to the speed of the belt. That requires a force.

3. Mar 7, 2009

### makeAwish

yah, so that force is the friction force?

4. Mar 7, 2009

### Staff: Mentor

The conveyor belt exerts a horizontal force on the sand, if that's what you mean by "friction force".

5. Mar 7, 2009

### makeAwish

hmm. okay!

then since they are moving at same speed can i say there is no resultant force on the system?

6. Mar 7, 2009

What system?

7. Mar 7, 2009

### makeAwish

the system of sand and belt?

8. Mar 7, 2009

### Staff: Mentor

It's unclear what you mean by "sand and belt" as your system. All the sand?

Focus on a section of the belt alone. Since its speed remains fixed, the net force on it must be zero.

The falling sand is being accelerated by the belt, so there must be a net force on that sand during its acceleration.

9. Mar 7, 2009

### makeAwish

Oh. okay sorry, i was actually referring to the sand on belt and the belt itself. for this, is no net force?

10. Mar 8, 2009

### sganesh88

Strictly speaking, the belt DOES slow down a bit as the sand particles fall on it. As the belt exerts a force to speed up the sand, the sand exerts an equal and opposite force on the belt slowing it down.

11. Mar 8, 2009

### Staff: Mentor

Since the belt maintains a constant speed, the net force on it is zero. Since the sand exerts a force on the belt, the mechanism must exert an equal and opposite force on the belt to maintain its constant speed.

12. Mar 8, 2009

### sganesh88

Ya. But i think, the belt should slow down for a very small interval of time before getting 'reinforcements' from the motor to maintain the speed.

13. Mar 8, 2009

### arildno

First lesson:

NEVER, EVER, break the PREMISE given in the exercise!

You are GIVEN that the velocity is constant, so that is what you are to assume for the remainder of the exercise.

Besides, STRICTLY speaking, you'd have to take into account relativistic and quantum mechanical effects, at least after you have included the gravitational effects from the planets impinging upon the scenario.

How do you know that these would be insignificant compared to the error source you happened to mention?