Question

The normal force equals the magnitude of the gravitational force as a roller coaster car crosses the top of a 33-mm-diameter loop-the-loop. Part A What is the car's speed at the top? Express your answer to two significant figures and include the appropriate units.

Answer 1

v = 0.56 m/s

Step-by-step explanation:

When passing the loop-the-loop, the car is making circular motion.

where R = 33/2 = 16.5 mm = 0.0165 m.

The acceleration can be found by Newton’s Second Law: F = ma.

At the top of the loop-the-loop: F = N + mg = 2mg.

Combining the two equations yields:

`2mg = m(v^2)/(R)\\</p><p>2g = (v^2)/(R)\\</p><p>2(9.8) = (v^2)/(0.0165)\\</p><p>v = 0.56~m/s`