Roller coaster cart gaining weight into a loop

[almightyfoon]

Homework Statement

A roller-coaster car starts from rest at a high point 2 times as high as the top of the loop-the-loop. When it is just about to enter the loop from the bottom, a 100 lb bag of bricks fall on the car, causing it to lose 25% of its speed. Neglecting friction, do you think the car will make it over the top of the loop wihtout falling off?
H=4R

Homework Equations

PE=mgh
KE=(1/2)mv^2
v=rω
a=rα

The Attempt at a Solution

m= mass of the cart
R= radius of the loop

I figured out the potential energy = 39.24Rm (9.81*4R*m)

Which means the KE at the bottom of the loop is the same thing. However the mass of the cart goes up by 100 lb (45.6 kg roughly) once the cart hits the loop. SO the KE=(1/2)(m+100)v^2.

I can solve for either of the variables, but that's a lot of algebra to do, and I don't really think its necessary. So... people of physics forum's, I have come from my lurking to beg for your help. This is the last problem of my homework set that's due at 9 AM.

 

[PeterO]

Homework Statement

A roller-coaster car starts from rest at a high point 2 times as high as the top of the loop-the-loop. When it is just about to enter the loop from the bottom, a 100 lb bag of bricks fall on the car, causing it to lose 25% of its speed. Neglecting friction, do you think the car will make it over the top of the loop wihtout falling off?
H=4R

Homework Equations

PE=mgh
KE=(1/2)mv^2
v=rω
a=rα

The Attempt at a Solution

m= mass of the cart
R= radius of the loop

I figured out the potential energy = 39.24Rm (9.81*4R*m)

Which means the KE at the bottom of the loop is the same thing. However the mass of the cart goes up by 100 lb (45.6 kg roughly) once the cart hits the loop. SO the KE=(1/2)(m+100)v^2.

I can solve for either of the variables, but that's a lot of algebra to do, and I don't really think its necessary. So... people of physics forum's, I have come from my lurking to beg for your help. This is the last problem of my homework set that's due at 9 AM.

We are now asking the cart plus sack to go through the loop.

The velocity has reduced to 3/4 of what it would have been had the sack been added before coming from the start.
if v is only 3/4, then the KE is only 9/16 - slightly more than half.
Relating KE at the bottom to PE at the start, as you did, you can find the height the loaded car has effectively started at.

Is that high enough for the car to make it through?