Finding radius of a loop using impulse and momentum

[dragonfall122]

Homework Statement

block 1 with mass of 680 g starts from rest at the top of a frictionless track at a height of
H = 4.20 M above the ground. Block 1 collides with block 2 (m = 175 g) at ground level. The blocks stick together and barely complete one turn around a frictionless loop. find the radius of the loop.

Homework Equations

p = mv
mg = mv²/r
U_i + K_i = U_f + K_f
J₁ + J₂ = 0

The Attempt at a Solution

I found the velocity of block 1 using conservation of evergy,
U_i + K_i = U_f + K_f
Ki = 0 because the object is at rest and and Uf = 0 because the object is at height = 0, so
U_i = K_f
so mgh = 1/2mv^2 so V = 9.07 m/s before the collision.

I used that velocity to find it's momentum,
p=mv so p= (.680 kg)(9.07 m/s)
so p is 6.17 kgm/s immediately before the collision.

I know that at the top of the loop the normal force working on the two objects is zero, and a FBD shows that the sum of the forces working in the y direction are mg = mv²/r

I know that block 2 has no impulse or momentum before the collision because its at rest.
I know that somehow I'm supposed to find the velocity of the two blocks after the collision, but I don't know how.

 

[MillerGenuine]

I know that at the top of the loop the normal force working on the two objects is zero, and a FBD shows that the sum of the forces working in the y direction are mg = mv2/r

Yes this is the correct equation to solve for Radius.

I know that block 2 has no impulse or momentum before the collision because its at rest.
I know that somehow I'm supposed to find the velocity of the two blocks after the collision, but I don't know how.

To find the final velocity you need to use conservation of momentum.
So P1i + P2i = P1f + P2f
the left side of the equation should be easy for you to solve..Just plug in your values. the right hand however takes some manipulation. You have
P1f + P2f and this gives us m1V1f + m2V2f
We know that after the collision the two masses will have the same velocity (because they are stuck together), so we can re-write the equation to look like V(m1+m2). This V is the velocity for both masses stuck together after the collision. Now we have
P1f + P2f = V(m1+m2). Then solve for V
Hope this helps

 

[dragonfall122]

Yes this is the correct equation to solve for Radius.


To find the final velocity you need to use conservation of momentum.
So P1i + P2i = P1f + P2f
the left side of the equation should be easy for you to solve..Just plug in your values. the right hand however takes some manipulation. You have
P1f + P2f and this gives us m1V1f + m2V2f
We know that after the collision the two masses will have the same velocity (because they are stuck together), so we can re-write the equation to look like V(m1+m2). This V is the velocity for both masses stuck together after the collision. Now we have
P1f + P2f = V(m1+m2). Then solve for V
Hope this helps

okay, for some reason my brain doesn't want to follow this.
p1_i = (.680)(9.07) = 6.17 kgm/s
p2_i = 0 because there is no velocity so I would I get
6.17 = V(m1 +m2) so
v= 6.17/ (m1 +m2) ?

 

[MillerGenuine]

p1i = (.680)(9.07) = 6.17 kgm/s
p2i = 0 because there is no velocity so I would I get
6.17 = V(m1 +m2) so
v= 6.17/ (m1 +m2) ?

Yes it will be your initial momentum divided by the sum of the masses.

okay, for some reason my brain doesn't want to follow this.

Is there something you still don't understand? make sure you understand how this problem is done. Conservation of momentum is an important concept in mechanics..& you should know how to maniupulate the Conservation of Momentum equation very well. So do some practice.

 

[dragonfall122]

Yes it will be your initial momentum divided by the sum of the masses.


Is there something you still don't understand? make sure you understand how this problem is done. Conservation of momentum is an important concept in mechanics..& you should know how to maniupulate the Conservation of Momentum equation very well. So do some practice.

it certainly seems that way. When I get my final equation and plug in numbers I keep getting the wrong answer and I'm not sure where my mistake is. I've emailed my professor to see if the mistake is on his part or on mine.

Thanks so much for you help!
dragonfall122