How Does Centripetal Force Affect Roller Coaster Dynamics?

[dontcare]

A roller-caster vechicle has a mass of 500 kg when fully loaded with passengers (Fig p7.28) (a) If the vechile has a speed of 20.0 m/s at point A, what is the force of the track on the vehicle at this point? (b) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the track?

a) $$a_{c} = \frac{v^2}{r} = 40 m/s^2$$

 

[nrqed]

A roller-caster vechicle has a mass of 500 kg when fully loaded with passengers (Fig p7.28) (a) If the vechile has a speed of 20.0 m/s at point A, what is the force of the track on the vehicle at this point? (b) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the track?

a) $$a_{c} = \frac{v^2}{r} = 40 m/s^2$$

Draw a free body diagram. Identify all the forces. The acceleration will be toward the center of the circle (where is the object here? I am assuming that it`s at the very top of a loop? In that case you would have $a_y = - v^2/R$). Then apply Newton`s second law.