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1) A force F = A/t^2 acts on an object. At time t = t_o its momentum is 0. What is its momentum after a very long time?

First I used Newton's second law:

dP/dt = A/t^2

Then

t^2 dP = A dt

dP = A/t^2 dt

And I took the integral of both sides, the left from 0 to P, the right from t_o to t...

P = -A/t + A/t_o

So as t-> infinity, P -> A/t_o. That's what I got. Is this correct?

2) Picture: http://www.brokendream.net/xh4/com.JPG

A wire is bent like a triangle with side lengths d at 45 degrees from the horizontal.

What is the y co-ordinate of the center of mass?

What I thought to do is to treat the center of mass as the centroid, taking the elements to be the length of each wire.

So I did:

y_com = [d*(d sin 45)/2 + d*(d sin 45)/2]/(2d) = (d sin 45)/2 = 0.35355d.

Is this correct?

3) Picture: http://www.brokendream.net/xh4/kidswing.JPG

With what force must the child pull down on the string if the combined mass of the child and the swing is W? Neglect friction from the pulley.

I'm guessing, from F = ma, 2T - W = 0 and thus T = W/2 is the force?

Thank you.

First I used Newton's second law:

dP/dt = A/t^2

Then

t^2 dP = A dt

dP = A/t^2 dt

And I took the integral of both sides, the left from 0 to P, the right from t_o to t...

P = -A/t + A/t_o

So as t-> infinity, P -> A/t_o. That's what I got. Is this correct?

2) Picture: http://www.brokendream.net/xh4/com.JPG

A wire is bent like a triangle with side lengths d at 45 degrees from the horizontal.

What is the y co-ordinate of the center of mass?

What I thought to do is to treat the center of mass as the centroid, taking the elements to be the length of each wire.

So I did:

y_com = [d*(d sin 45)/2 + d*(d sin 45)/2]/(2d) = (d sin 45)/2 = 0.35355d.

Is this correct?

3) Picture: http://www.brokendream.net/xh4/kidswing.JPG

With what force must the child pull down on the string if the combined mass of the child and the swing is W? Neglect friction from the pulley.

I'm guessing, from F = ma, 2T - W = 0 and thus T = W/2 is the force?

Thank you.

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