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**Help please! simple Physics frictionless crate on ramp problem! Urgent!?**

A crate of mass m = 100 kg is pushed at constant speed up a frictionless ramp (θ = 30.0°) by a horizontal force F. What are the magnitudes of (a) F and (b) the force on the crate from the ramp?

So my teacher did this problem but I do not understand

here's what he did:

a) mg sin θ = 100(9.8)sin30 = 490 N (I understand this part)

490 / cos30 = 566N <--Why divide by cos 30 to get the correct answer?!?

b) N = mg cos θ + F sin θ

100(9.8)cos30 + 566sin30 = 1131N <--I do not understand part b) at all. Can someone explain step by step on what we are doing on part b).

help please!