Question

What is the acceleration of a 45kg block at rest pushed by a 280N horizontal force up to 30degree inclined planw with a roughness coefficient of 0.15

Answer 1

1) Determine the normal force:

$$N=mg\cos\theta+F\sin\theta.$$

2) The force of friction:

$$f=\mu N=\mu(mg\cos\theta+F\sin\theta).$$

3) The net force:

$$F_\text{net}=F\cos\theta-f,\\\space\\ F_\text{net}=F\cos\theta-\mu(mg\cos\theta+F\sin\theta)=164\text{ N}.$$

4) Calculate the acceleration:

$$a=F_\text{net}/m=3.64\text{ m/s}^2.$$