# Impule & Momentum

## Homework Statement

Note Diagram.

If they are released from rest, determine the time required for block A to attain a speed of 2 m/s. Neglect the mass of the ropes

## The Attempt at a Solution

I = mk2 = (30)(.252) = 1.875 kg m2

X Direction

mv + $$\int$$ Fdt = mv2

0 + Oxt = 0

Y Direction

mv + $$\int$$ Fdt = mv2

0 + Oyt - 30(9.81)t = 0

Oy = 294.3

Moments

Iw1 + $$\int$$MOdt = Iw2

0 + 25(.3) - 10(.18) = 1.875w2

w = $$\sqrt{3.04}$$

How do i relate this to velocity and time. I can use v = wr, but how can i solve for t when v = 2 m/s

2 = .3w, therefore i need to find t when w = 2/.3

#### Attachments

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I'm having trouble understanding the image. Can you get a better one or explain the image further?
Anyway, it seems you are making things much more complicated than they have to be.
Draw a FBD, and apply Newton's second law in linear and angular forms to each mass. The rest should just be kinematics.

The spool has two radiuses. one is .18m and one is .3m. they start from rest. when the blocks are released, block A weighs more so it will fall, thus lifting block B. When will block a reach a speed of 2 m/s.

But ya i dont think i needed most of what i posted first. Heres what im at

I = mk2 = 30(.25)2 = 1.875

25(.3) - 10(.18) = 1.875w2

w = $$\sqrt{3.04}$$

w = v/r

$$\sqrt{3.04}$$(.3) = v

how do i get a t in there

I think that I would take a different approach. You know that

$$\sum M =I\alpha$$

and there is a relationship between alpha and the acceleration of the blocks.

So you can write the sum of the moments in terms of a

Since $a=\frac{dv}{dt}$ you should be able to find t using the initial conditions.

Edit: Was there a reason you thought that it was an Impulse & Momentum problem? I am only wondering in case I overlooked something.

okok i think i got it

I = 1.875

Iw2 + + $$\sum\int$$Mdt = Iw2

0 + $$\int$$(25(.3) - 10(.18)dt = 1.875w2

5.7t = 1.875w2 therefore w = $$\sqrt{3.04t}$$

w = v/r

$$\sqrt{3.04t}$$(.3) = v = 2

3.04t = 4

t = 1.32 seconds

Is this right

I thought it was impulse and momentum because the chapter is called

Planar Kinetics of a Rigid Body: Impulse and Momentum
Section 19.2 Principle of Impulse and Momentum

Im assuming there is more than one way to solve it, im just suppose to use impulse and momentum

Edit: I can multiply :rofl: I think you're good!

You can always do it the other way as a check.

You have all the numbers necessary.

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but u do agree with my answer based on my method