Answer to Question #274413 in Physics for dodo

Question

Suppose that a force F=250 N applied at 20° below the horizontal is just enough to start the motion of the 55 kg crate in Sample Problems 3.5 item 3. Find the (a) normal force and (b) coefficient of static friction. please explain it by step-by-step with explanation THANK YOUUU

Answer 1

(a) Find the normal force applying Newton's second law:

$$0=N-mg-F\sin\theta,\\\space\\ N=mg+F\sin\theta=625\text{ N}.$$

(b) Find the force required to just start moving the crate. We remember that this force is equal to the force of static friction:

$$F\cos\theta=f,\\ f=\mu N,\\\space\\ \mu=\frac fN=\frac{F\cos\theta}N=0.376.$$