Physics calculation- does anyone understand the solution to this question?

I don't understand this physics?

• I have found a contradiction in my physics, and I need help understanding why I made this mistake. (For simplicity purposes I will only state the part of the question I have trouble with, not the entire question). Question 1 is: A block with a mass m starts falling down a slope that is banked at theta degrees. What is the normal force of the block ? My solution: mass*gravity*sin(theta). This appears correct. Furthermore, assuming no coefficient of friction, the frictional force is mass*gravity*cos(theta). The next question's solution appears to be the exact opposite Question 2: A car with mass m is on a banked highway curve (ie. the road is not flat) of theta degrees. What is the normal force of the car? My solution: n*cos(theta) = mg n = mg/cos(theta) This is also correct.. So how come the normal force is sin for the first question, but cos for the second question

• Answer:

  Question 1. normal force of the block on the sloping path = mg cos theta, whether frictions acts or does not act. The cause for this force is earths pull on the block. mg sin theta is the earth's pull on the block tangential to the surface of the slope in which direction it is free to move. Same argument works for the car at rest on the banked road, for the normal force by the car on the road. only difference is that on a banked road, the car travels on a circular path in the horizontal plane. Now the force due to earth cannot have any component in a direction perpendicular to the vertical force. But the reaction, N (which is adjustable, it need not be always mg cos theta) of the road can have. N cos theta is the force which provides centripetal force to the car to move in a circle. but that is altogether a different consideration.