# F=ma ?

1. Sep 23, 2006

### Joules23

A man is standing on a platform that is connected to a pulley arrangement, as the drawing shows. By pulling upward on the rope with a force P the man can raise the platform and himself. The total mass of the man plus the platform is 94.0 kg. What pulling force should the man apply to create an upward acceleration of 1.20 m/s2?

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F=(m)(ay), right?
however i see that i have two Y component accelerations, gravity, wich is -9.8, and the upward acceleration we are trying to reach, so now do i just do:
a=-9.8 +1.2 = -8.6
F=(94kg)(-8.6)
F=-808.4
i guess u cant have a negative? so anser is 808.4N
did i do this right?

2. Sep 23, 2006

### Andrew Mason

There is only one acceleration: it is up at 1.2 m/sec^2. The sum of the forces must equal the mass of the platform and man x that acceleration. So start by setting out those forces and setting them equal to the mass x acceleration.

AM

3. Sep 23, 2006

### Joules23

m=94kg
a=1.2 m/s^2
F=ma
F=112.8

like that?

4. Sep 23, 2006

### Andrew Mason

That is the net force acting on the platform (in Newtons). But you are asked to find what force the man must exert on the rope.

Look at all the downward forces: what are they?

Look at all the upward forces: what are they? (hint: what is the tension in the rope?)

Add them up and the must equal 112.8 N.:

$$\vec{F_{up} } + \vec{F_{down}} = m\vec a$$

AM

5. Sep 23, 2006

### Joules23

ok i think i got it, please let me know if i do....

T+T-W=112.8
2T-921.2=112.8
2T=1034
T=517=Upward Force
517+x=112.8
x=-404.2=Downward Force

6. Sep 24, 2006

### Andrew Mason

x is not the downward force. The downward force is W. You are trying to find T. Your answer for T is correct. [edit: T is not correct - see Doc Al's post and correction below]

It is better to work it out algebraically then plug in numbers.

$$2\vec{T} + m\vec g = m\vec a$$

(Up is positive. Down is negative)

$$T = m(a + g)/2$$

AM

Last edited: Sep 24, 2006
7. Sep 24, 2006

### Staff: Mentor

The upward force on the "man + platform" is T, not 2T.

8. Sep 24, 2006

### Andrew Mason

Of course you are right. It should be:

$$T - W = ma$$

$$T = m(g+a)$$

AM

9. Sep 24, 2006

### Poop-Loops

I'm scared that I'm not understanding what all the fuss is about...

Why wouldn't it just be:

(9.8 + 1.2) x 94kg?

10. Sep 24, 2006

### Mindscrape

It is that, but do you really understand why?

11. Sep 24, 2006

### Poop-Loops

Of course.

You need to supply force so you + pully don't drop down, and then extra force to actually accelerate yourself up.