Answer:
(a) [tex]f_k=97.1N[/tex]
(b) [tex]a=1.10m/s^{2}[/tex]
Explanation:
First, we write the equations of motion of the crate for each axis:
[tex]x: F-f_k=ma\\\\y:N-mg=0[/tex]
Since the kinetic frictional force is equal to [tex]\mu N[/tex], and from the second equation we have that:
[tex]f_k=\mu N=\mu mg\\\\f_k=(0.150)(66.0kg)(9.81m/s^{2})=97.1N[/tex]
This means the frictional force has a magnitude of 97.1N (a).
Next, we use this value to calculate the magnitude of acceleration from the first equation of motion:
[tex]a=\frac{F-f_k}{m} \\\\a=\frac{170N-97.1N}{66.0kg}=1.10m/s^{2}[/tex]
In words, the magnitude of the crate's acceleration is 1.10m/s² (b).
