Question

A man is sitting on a roller coaster and is at the top of a circular loop (He is upside down at this point.) where he is pushing against his seat with a force that is exactly equal to his weight.
What is his vertical acceleration at this point, in terms of g, the acceleration of gravity?

• A. g downward
• B. g upward
• C. $2g$ downward
• D. $2g$ upward
• E. $0g$

Answer 1

Answer: (C)

$2g$ downward

At the top of roller coaster:

The net force to the center (downward),

$F=R+W$

where $R=$ normal reaction on man in downward direction

$W=$ weight of man in downward direction

hence, $F=R+mg$

but given: $R=mg$

therefore $F=mg+mg=2mg$

$ma=2mg$

or $a=2g$ in downward direction