Question

A child goes down a playground slide that is inclined at an angle of 27.5° below the horizontal. Find the acceleration of the child given that the coefficient of kinetic friction is .415?

A) 4.82 m/s^2
B) 5.10 m/s^2
C) 6.04 m/s^2
D) 4.15 m/s^2.

Answer 1

The acceleration of the child going down the slide is approximately 4.82 m/s².

Step-by-step explanation:

To find the acceleration of the child going down the slide, we can use the forces acting on the child. The force parallel to the slide is given by the weight of the child, which is mg, where m is the mass of the child and g is the acceleration due to gravity. The force of friction is given by the coefficient of kinetic friction times the normal force, which is mg*cos(θ), where θ is the angle of inclination. The net force is the difference between the force parallel to the slide and the force of friction, which is equal to mass times acceleration. So, we have:

mg*sin(θ) - mg*cos(θ)*μ = ma

Simplifying and plugging in the values, we get:

a = g*(sin(θ) - μ*cos(θ))

Substituting θ = 27.5° and μ = 0.415, we can calculate the value of a to be around 4.82 m/s².