Forces and Pulleys problem Help due in the morning

[BlasterV]

Construction worker Fred, who has a mass of 96 kg, stands on a girder. He sees a sandbag of mass 33 kg sitting on the ground, a distance 12 m below. A massless rope tied to the sandbag runs up and over a frictionless pulley connected to the girder. "Aha!", says Fred, "I'll lower myself to the ground gently by grabbing the rope. I'll fall slowly to the ground while the sandbag rises up to the girder. Brilliant!"

How fast will Fred be moving when he reaches the ground?

Ok. Now, I assume velocity is negative, since the man is "falling"/moving down.

To find acceleration down I thought it would be Force down over the summation of weight: i.e.
(9.8 m/s^2 * 96kg) / (96 + 63) = 5.9169 m/s^2

Then, I need his velocity when he reaches the ground, i.e.: V final.

Vf^2 = Vi^2 + 2ad

Vf^2 = 0^2 + 2 (5.9169 m/s^2)(12)
Vf^2 = 142.0075
Vf = 11.9166 m/s

Since the man is using the pulley to move DOWN, the position is going negative and thus velocity must be negative (I think? :( )

Vf = -11.9166 m/s

The "online-homework grader" is saying my answer is wrong, can anyone tell me where I messed up and how to fix it?

 

[cyby]

Construction worker Fred, who has a mass of 96 kg, stands on a girder. He sees a sandbag of mass 33 kg sitting on the ground, a distance 12 m below. A massless rope tied to the sandbag runs up and over a frictionless pulley connected to the girder. "Aha!", says Fred, "I'll lower myself to the ground gently by grabbing the rope. I'll fall slowly to the ground while the sandbag rises up to the girder. Brilliant!"

How fast will Fred be moving when he reaches the ground?

Ok. Now, I assume velocity is negative, since the man is "falling"/moving down.

To find acceleration down I thought it would be Force down over the summation of weight: i.e.
(9.8 m/s^2 * 96kg) / (96 + 63) = 5.9169 m/s^2

Then, I need his velocity when he reaches the ground, i.e.: V final.

Vf^2 = Vi^2 + 2ad

Vf^2 = 0^2 + 2 (5.9169 m/s^2)(12)
Vf^2 = 142.0075
Vf = 11.9166 m/s

Since the man is using the pulley to move DOWN, the position is going negative and thus velocity must be negative (I think? :( )

Vf = -11.9166 m/s

The "online-homework grader" is saying my answer is wrong, can anyone tell me where I messed up and how to fix it?

well, just be consistent in how you set up your axes. If you would like your velocity to be negative downwards, then so is gravity (which acts downwards too)

Now, the other thing.. is that.. you said the sandbag is 33kg, but you wrote 63 in your equation.. did you make an arithmetic mistake, or is there more?

 

[BlasterV]

oh my bad, the sandbag is 63 not 33, that's a typo :(

I don't know what I did wrong or what to do though, do you know how this is suppose to work?

 

[cyby]

Well, did you draw your Force diagram? Can you show it to us? Then maybe we can deal with the mathematics...

 

[BlasterV]

uhm, that's hard to do with ASCII...
a pulley.

/o\
| | 96kg man going DOWN, Gravity pushing both objects DOWN (obviously)
|
|63kg sandbag going UP

Height = 12m

Thats about the best I can show

 

[cyby]

I know how it looks like. I am asking you to draw a free-body diagram so you can use Newton's second law to find the net force. You can draw it/scan it in and then post a link or use an attachment or something.

 

[BlasterV]

ok is this what you meant?

 

[cyby]

Ok, good. Now, we see that the net force is (mass of man - mass of sandbag) * gravity. Note that I subtracted the masses because the forces are in opposite directions.

Now try again and see what you get :-)

 

[BlasterV]

If I do that I get ( 96 kg - 63kg ) = 33 kg

33 kg * 9.8m/s^2 = 323.4 N

In order to solve for a velocity I need an acceleration don't I? so how can I go farther if I do it like this?

 

[cyby]

You have a net force, and so you will have a net acceleration on the system as well.

 

[BlasterV]

So net acceleration would be:

NetForce = NetMass * NetAccel
323.4 N = 159 kg * NetAccel
324.4N/159kg = netaccel
2.03396226415 m/s^2 = netaccel

Vf^2 = vi^2 + 2ad

Vf^2 = 0^2 + 2(netaccel)(12)

Vf^2 = 48.8150943396
Vf = 6.98677996932 m/s when hitting ground

Velocity must be negative!

So final answer is -6.98677996932 m/s, right? or did I do something wrong again?

 

[cyby]

Again, please be consistent. If you have a positive Net Force, and it is pointing downwards, your velocity and acceleration vectors should also point downwards. (You used a positive net force downwards)...

So you should have a positive velocity downwards. I won't check your numbers, but your concepts appear sound.

 

[BlasterV]

Can anyone please confirm if my answer is correct? thanks!

 

[Andrew Mason]

Can anyone please confirm if my answer is correct? thanks!

When Fred leaves the girder he has initial KE before the rope has any tension.
It is much easier to do this by analysing the energy.

$$\Delta PE = \Delta KE$$

$$(M-m)gh = 1/2 (m+M) v^2$$

$$v^2 = 2(M-m)gh/(m+M)$$

h represents the change in height of Fred's center of mass (assuming he does not bend his knees when landing) which is the same as that of the sandbag.

AM