Answer to Question #127543 in Classical Mechanics for nit

Question

A 50.0 kg crate is at the top of a ramp that makes a 30o angle with level ground. If the crate starts to slide and the coefficient of kinetic friction between the crate and the ramp is 0.42, what is the acceleration of the crate?

Answer 1

As per the question,

Mass of the crate $(m)= 50 kg$

Angle of the ramp with the ground level $(\theta)=30^\circ$

Coefficient of the kinetic friction $(\mu_k) = 0.42$

Acceleration of the crate $(a) = ?$

Now,

$\Rightarrow ma=mg\sin\theta -f_s$

Now, substituting the values,

$a=\frac{mg\sin\theta-\mu_k mg\cos\theta}{m}=\frac{mg(\sin 30^\circ -0.42\times \cos30^\circ)}{m}$

$a=9.8\times 0.3 =2.94 m/sec^2$