Question

Direction: answer the following questions below.

1. A block of mass 1.0 kg rests on a horizontal surface. The frictional coefficients for the block and surface are μs=0.50 and 40.μk=0.40. (a) What is the minimum horizontal force required to move the block? (b) What is the block’s acceleration when this force is applied?
2. The coefficient of kinetic friction between the board and the snow is 0.20. 10.0°𝜇𝑘 = The snowboarder is now moving down a hill with incline. What is the skier’s acceleration?

Answer 1

1. (a) The minimum horizontal force required to move the block is

$$F=\mu_smg=0.5·1·9.8=4.8\text{ N}.$$

(b) The acceleration is

$$a=\frac {F-\mu_kmg}m=\frac {F}m-\mu_kg=0.88\text{ m/s}^2.$$

2. The acceleration can be found by a special equation derived from the application of Newton's second lae to the given problem:

$$a=g(\sin\theta+\mu_k\cos\theta)=3.63\text{ m/s}^2.$$