# What force is needed to produce a constant speed?

1. Aug 12, 2013

### tjhero123

1. The problem statement, all variables and given/known data

An empty wagon with mass 10 kg is pulled by a force of 75 N at a constant speed. Rain falls collecting in the wagon at a rate of 375mm^3/s. The density of water is 1g/mm^3.
A) Make a table showing how much force must be exerted on the wagon to keep it moving at a constant speed for 10 seconds. Graph it.
B)Find the average force exerted on the wagon over this 10 second period.
C)What is the impulse over these 10 seconds?

2. Relevant equations
mass of wagon at time t (seconds) in kg=10+0.375t
F(net)=ma

3. The attempt at a solution
If the wagon is moving at a constant speed, then all forces must be balanced. So the 75 N force must be balanced by a friction force also of 75 N. The equation for mass of the wagon was simple enough to derive but im stuck at this part. Is this a trick question? Because the way i see it is that no aditional force is required to keep it moving at a constant speed. As long as the 75 N force was continued and balanced by the friction force, wouldnt the cart continue to move at a constant speed forever no matter how much mass was gained from the rain? So the average force exerted on the wagon would just be 75 for 10 seconds and therefore the impulse would be 750. Or does the 75 N force not even count as an exerted force since its balanced and the actual answer is 0?

2. Aug 12, 2013

### BruceW

Are you sure that the friction force doesn't depend on the mass of the cart? Do you know any equations for the friction force due to rolling friction?

3. Aug 12, 2013

### voko

Does the friction force stay constant as water accumulates on the wagon?

4. Aug 12, 2013

### tjhero123

The friction force is dependant upon the Normal force and coeffeiciant of friction. Is that correct? So would i calculate the coefficiant first with the normal force being = to 10(9.81) and the friction force equal to 75 N? Then as the mass increases the Fn will increase and i can multiply that by the coefficiant of friction that i get in the first part to get my new Friction force?

5. Aug 12, 2013

### voko

Replace the question marks with full stops, and you should be fine :)

6. Aug 12, 2013

### Staff: Mentor

Pardon my poking my nose in here, but is it being assumed that the raindrops have the same horizontal speed as the cart when they land? Seems a bit of a stretch... how do the raindrops "know" how fast they should be traveling in order to not affect the momentum of the cart? If the drops are falling vertically they will need to be accelerated to cart speed when they land.

Seems to me that the problem is more complicated than just dealing with an increase in friction...

7. Aug 12, 2013

### voko

That is a valid concern, but given the nature of the questions and the fact that the constant speed is not given, the problem apparently wants us to ignore that.

8. Aug 12, 2013

### Staff: Mentor

Yes, I suppose it does. But it's a pretty vague way to make it known.

9. Aug 14, 2013

### CWatters

What would the pressure be :-)

10. Aug 14, 2013

### howie8594

The density of water is not 1 g/mm^3