Question

A block of weight 100 N is against a vertical surface and acted upon by the given forces. What magnitude of force will accelerate it at 1 m/s2 up the surface? The coefficient of kinetic friction between block and surface is uk = 0.25.

Answer 1

The Newton's second law gives

$$N=F\sin 20\degree+P\sin 30\degree \\ ma=F\cos 20\degree-\mu_kN-P\cos 30\degree-mg$$

We get equation

$$ma=F\cos 20\degree-\mu_k(F\sin 20\degree+P\sin 30\degree)-\\ -P\cos 30\degree-mg$$

Hence

$$F=\frac{m(a+g)+P(\mu_k\sin 30\degree+\cos 30\degree)}{\cos 20\degree-\mu_k\sin 20\degree}$$ $$F=\frac{10(1+10)+5(0.25\sin 30\degree+\cos 30\degree)}{\cos 20\degree-0.25\sin 20\degree}$$

$$F=134\:\rm N$$