i cant figure this out

Question

A 3.00 kg block starts from rest at the top of a 30° incline and slides a distance of 1.90 m down the incline in 1.40 s.(a) Find the magnitude of the acceleration of the block.
 m/s2

(b) What is the coefficient of kinetic friction between block and plane?

Your response differs from the correct answer by more than 10%. Double check your calculations.

(c) What is the frictional force acting on the block?
Magnitude

 

(d) Find the speed of the block after it has slid 1.90 m.
 m/s

Answer 1

As in most cases of this type, it is convenient to define x axis along the incline and y axis perpendicular to it.

a) Since initial velocity is zero, it is convenient to use: Δx=V_oxt +(1/2)a_xt², and solve for acceleration

b) Need to draw a FBD (free body diagram) and use Newton's 2nd equation for x and y components: ΣF_x=ma_x and ΣF_y=ma_y . One key step is to decompose the weight correctly into x and y components using sin and cos trigonometric functions.

For the x direction you will probably have: mg*sin() - f = ma_x, where f is the frictional force force and you can solve for f from this equation. (answer to c).

Once you find f, use the fact that f=µ_kN, (where N is the normal force) and solve for the coefficient of kinetic friction µ_k

c) Solved above

d)Kinematics, use: v_f²=v_o²+2ad and solve for Vf.

Hope this is enough to have you solve the problem. If you have any questions, just let me know.