# B Fallrate calculation

1. Jul 31, 2016

### mrdans777

I'm trying to figure out how fast an object will fall/accelerate with a constant upward force applied to it. For instance, a 100 lb object with a 25 lb upward force applied to it. Would it fall/accelerate at the same speed as a 75 lb object?

2. Jul 31, 2016

### Aniruddha@94

Draw a free body diagram of the mass and use Newton's 2nd law i.e. , the sum of forces on it is equal to $ma$.
What do you think about it??

3. Jul 31, 2016

### Staff: Mentor

This is one of those problems where it helps to be careful about the distinction between force and mass. It's also easier to get it right if you use the metric system because the distinction between mass (in kilograms) and force (in newtons, and the gravitational force on a 1 kilogram mass is $9.8 \approx 10$ newtons) is explicit - American units blur the two concepts together with the word "pound".

So I'll restate it in metric units and I'll bet that you can work it out for yourself: does a 100 kilogram object subjected to an upward force of 250 newtons (the gravitational force on a 25 kilogram object) accelerate downwards more or less quickly than a 75 kilogram object in free fall? Calculate the net force on each, plug into $F=ma$, see what comes out.

4. Jul 31, 2016

### mrdans777

Thanks. What I get from these calculations is that fall rate would be the same in both instances. What trips me up is thinking about a helicopter or other VTOL aircraft descending straight down to land with a net mass of maybe 20 lbs or something, versus a 20 lb object. The helicopter comes down slowly but the object seems it would drop much faster, even initially, before acceleration becomes a factor.

5. Jul 31, 2016

### jbriggs444

Please do the calculations first and judge the results after.

6. Jul 31, 2016

### mathman

Free falling objects all fall at the same rate, irrespective of mass (ignoring air resistance) - Galileo experiment. Applying an upward force would slow it down. Net result it would fall slower than the free falling object.

7. Jul 31, 2016

### Staff: Mentor

If that's how the calculations came out, you made a mistake somewhere. Post your work and someone here will be able to spot the problem.