Question

At last year's Homecoming Pep Rally, Trudy U. Skool (attempting to generate a little excitement) slid down a 42.0 degree incline from the sports dome to the courtyard below. The coefficient of friction between Trudy's jeans and the incline was 0.650. Determine Trudy's acceleration along the incline.

Answer 1

Answer:

   a = - 1.8 m / s²

Explanation:

To solve this exercise let's use Newton's second law, let's start by defining a reference system with the x axis parallel to the plane, in the adjoint we can see a diagram of the forces

let's break down the weight

           sin 42 = Wₓ / W

           cos 42 = W_y / W

           Wₓ = W sin 42

            W_y = W cos 42

     

Y axis  

     N- W_y = 0

     N = W_y

     N = mg cos 42

X axis

     fr -Wₓ = m a

     a = (fr - mg sin 42) / m

the friction force has the formula

    fr = μ N

    fr = μ mg cos 42

we substitute

    a = (μ g cos 42– g sin 42)

    a = g (μ cos 42 - sin 42)

   

let's calculate

    a = 9.8 (0.650 cos 42 - sin 42)

    a = - 1.8 m / s²

The negative sign indicates that the acceleration is downward, so the boy is descending.