brakes go to floor, pulling rt, shaking... caliper? Nope

[bikerchick4God]

Those symptoms point to a frozen caliper right? and yet upon inspection today brake fluids full; none leaking on the tire (I had a froz caliper yrs ago on a Pontiac).
My neighbor, THANK YOU TOM, came over and checked the obvious. What he found was a broken vacuum line to a part I can't identify.
Can someone please tell me what this cylindrical shaped part is? After Tom replaced the line and about 20 brake pumps, she's back to normal.
Thanks for your help.

 

[Centaurious]

That is the vacuum reservoir for the heater controls, it has nothing to do with the brakes.

Pumping the pedal 20 times got you pressure back. WHY did you loose pressure in a closed system like your brakes? Until you can answer this I would be very reluctant to drive it.

I've lost the brakes just once in my life and fortunately it was right in front of my workplace and going 15 mph. The hard line to the front brakes wore on a bracket and blew open just then. It could have happened in traffic and been disastrous.

 

[974X4BLACKSPORT]

If your brake pedal goes to the floor, you either have a real bad leak, lots of air in the lines (which points to a leak), or the master cylinder is bad.

 

[410Fortune]

BAD master cylinder, no way around it
Vacuum booster is a booster, you should still have a brake pedal without the power assist of the booster.
If the pedal hits the floor and fluid is not leaking = you need a new master cylinder