Answer :
Answer:
The acceleration is [tex]a = 6.2 m/s^2[/tex]
Explanation:
From the question we are told that
The angle which the inclined plane make with horizontal is [tex]\theta = 0.44 \ rad[/tex]
The frictional coefficients are [tex]\mu_{\mu s} = 0.61[/tex] and [tex]\mu_{\mu k} = 0.23[/tex]
The force acting on the crate is mathematically represented as
[tex]f = F_w + F_N[/tex]
Here f is the net force at which the crate is sliding down the plane which is mathematically represented as
[tex]f = ma[/tex]
[tex]F_w[/tex] is the force due to weight which is mathematically represented as
[tex]F_w = mg sin (\theta)[/tex]
and [tex]F_N[/tex] the force due to friction which is mathematically represented as
[tex]F_N = \mu_{\mu k } * mg cos(\theta )[/tex]
So
[tex]ma = mgsin(\theta ) + \mu_{\mu k} mg cos(\theta )[/tex]
[tex]a = gsin(\theta ) + \mu_{\mu k } * g cos(\theta)[/tex]
substituting values
[tex]a = 9.8 sin(0.44 ) + 0.23 * 9.8* cos(0.44)[/tex]
[tex]a = 6.2 m/s^2[/tex]