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Query with forces in 2 dimensions

I understand how to get angles and forces in a scenario where a particle of X mass is being pulled up a slope of θ° with a force of F, but now a friction force is also involved, usually parallel to the slope. How do I go about including this additional force in equations.

Example: A mass of 20kg is being pulled up a slope at 14° to the horizontal. A force of 70N pulls the object at an angle of θ° at a constant speed, despite the 10N of friction. Find θ

I tried 70cos(θ) = 200sin(14) but that answer is slightly off, so I know I need to incorporate the 10N of friction somewhere, but I'm not sure how.

Reply 1

mscully

if you resolve the forces going up the slope using f=ma you would get 70cos(theta)-20gsin(14)-10=0
you just need to include all the forces, positive and negative that are acting in the direction you are resolving