A block with mass m1 = 9.4 kg is on an incline with an angle θ = 25° with respect to the horizontal. For the first question there is no friction, but for the rest of this problem the coefficients of friction are: μk = 0.22 and μs = 0.242. 1) When there is no friction, what is the magnitude of the acceleration of the block?

a = 4.14 m/s²

Explanation:

We calculate the weight component parallel to the displacement of the block:

We define the x-axis in the direction of the inclined plane, 25° to the horizontal.

W = m*g : Total block weight

Wx = W*sen25° = m*g * sen25°

We apply Newton's second law:

∑F = m*a (Formula 1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Problem development

We apply the formula (1) to calculate the acceleration of the block:

∑Fx = m*a

Wx = m*a

m*g * sen25° = m*a : We divide by m on both sides of the equation

g * sen25° = a

a = g * sen25° = 9.8 * sen25° = 4.14 m/s²